An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges
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paper_title: A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design

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The experimental design technique is used for the weight assignment.A mathematical model is constructed to help the DMs make reasonable decisions.Different MCDM evaluation methods are combined to solve the same MCDM problem.The top-ranked alternatives exactly match with those derived by the past researchers. Multiple criteria decision-making (MCDM) is a difficult task because the existing alternatives are frequently in conflict with each other. This study presents a hybrid MCDM method combining simple additive weighting (SAW), techniques for order preference by similarity to an ideal solution (TOPSIS) and grey relational analysis (GRA) techniques. A feature of this method is that it employs an experimental design technique to assign attribute weights and then combines different MCDM evaluation methods to construct the hybrid decision-making model. This model can guide a decision maker in making a reasonable judgment without requiring professional skills or extensive experience. The ranking results agreed upon by multiple MCDM methods are more trustworthy than those generated by a single MCDM method. The proposed method is illustrated in a practical application scenario involving an IC packaging company. Four additional numerical examples are provided to demonstrate the applicability of the proposed method. In all of the cases, the results obtained using the proposed method were highly similar to those derived by previous studies, thus proving the validity and capability of this method to solve real-life MCDM problems.
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paper_title: Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets

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Abstract In real life, it is not always the case that experts are able to assess alternatives by precise values. With the incomplete and vague information obtained, the experts are inclined to provide their assessments by eliciting linguistic terms. Considering that the experts may hesitate between several linguistic terms during the evaluating process, a new tool called the hesitant fuzzy linguistic term set (HFLTS) was introduced to represent this situation. This tool allows the experts to use several possible linguistic terms rather than a single one to appraise the performances of alternatives. In this paper, we investigate the ELECTRE II method in the HFLTS environment and propose two new approaches named the score-deviation-based ELECTRE II method and the positive and negative ideal hesitant fuzzy linguistic elements based ELECTRE II method. To fully explore the underlying preference information and specify the outranking degrees of alternatives, we set up three levels of concordance and discordance sets, which are finally devoted to ranking the alternatives more convincingly. An illustrative example is operated to show the practicability of the proposed methods and then a sensitivity analysis is performed as well to test the robustness of the two methods.
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paper_title: An interval type-2 fuzzy PROMETHEE method using a likelihood-based outranking comparison approach

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We develop an interval type-2 fuzzy PROMETHEE method to address MCDA problems.The proposed method uses the approach of likelihood-based outranking comparisons.We present novel likelihood-based preference functions based on outranking indices.We develop two algorithmic procedures to acquire partial and complete rankings.Comparative analysis validates the effectiveness of the proposed method. Based on the preference ranking organization method for enrichment evaluations (PROMETHEE), the purpose of this paper is to develop a new multiple criteria decision-making method that uses the approach of likelihood-based outranking comparisons within the environment of interval type-2 fuzzy sets. Uncertain and imprecise assessment of information often occurs in multiple criteria decision analysis (MCDA). The theory of interval type-2 fuzzy sets is useful and convenient for modeling impressions and quantifying the ambiguous nature of subjective judgments. Using the approach of likelihood-based outranking comparisons, this paper presents an interval type-2 fuzzy PROMETHEE method designed to address MCDA problems based on interval type-2 trapezoidal fuzzy (IT2TrF) numbers. This paper introduces the concepts of lower and upper likelihoods for acquiring the likelihood of an IT2TrF binary relationship and defines a likelihood-based outranking index to develop certain likelihood-based preference functions that correspond to several generalized criteria. The concept of comprehensive preference measures is proposed to determine IT2TrF exiting, entering, and net flows in the valued outranking relationships. In addition, this work establishes the concepts of a comprehensive outranking index, a comprehensive outranked index, and a comprehensive dominance index to induce partial and total preorders for the purpose of acquiring partial ranking and complete ranking, respectively, of the alternative actions. The feasibility and applicability of the proposed method are illustrated with two practical applications to the problem of landfill site selection and a car evaluation problem. Finally, a comparison with other relevant methods is conducted to validate the effectiveness of the proposed method.
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paper_title: Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis

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Abstract The aim of this paper is to develop novel VIKOR-based methods for multiple criteria decision analysis involving Pythagorean fuzzy information. The concept of Pythagorean fuzzy sets possesses definite advantages in handling vagueness and complex uncertainty over well-known nonstandard fuzzy sets, such as intuitionistic fuzzy sets and interval-valued fuzzy sets. Taking the powerfulness of Pythagorean fuzzy sets into account when tackling imprecise and ambiguous information in multiple criteria decision-making problems, this paper proposes remoteness index-based Pythagorean fuzzy VIKOR methods, which are significantly different from the existing VIKOR techniques. The uniqueness of the proposed VIKOR methodology is the consideration of uncertain information represented by Pythagorean fuzzy values and the construction of certain valuable concepts of a generalized distance measure and displaced and fixed remoteness indices. A flexible and multipurpose definition of a distance measure for Pythagorean fuzzy information is presented based on the Minkowski distance model. The generalized Pythagorean fuzzy distance measure presented in this paper is then applied to establish useful concepts of remoteness indices, consisting of displaced positive- and negative-ideal remoteness indices as well as fixed positive- and negative-ideal remoteness indices. Unlike the canonical VIKOR ranking procedure, this paper provides a new way to rank candidate alternatives and determine the compromise solution depending on distinct preference structures for adapting to the particularities within the Pythagorean fuzzy environment. Several useful multiple criteria ranking indices, consisting of remoteness-based group utility, individual regret, and compromise indices, are developed to facilitate compromise ranking among alternatives. Four algorithmic procedures of the presented remoteness index-based Pythagorean fuzzy VIKOR methods are also provided in detail. Furthermore, some real-world applications and comparative analyses concerning a criteria satisfaction problem, two service quality and Internet stock performance evaluation problems, and two Internet stock and R&D project investment problems are conducted to demonstrate the effectiveness and advantages of the proposed methods in practice.
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paper_title: FLM-TOPSIS: The fuzzy linguistic multiset TOPSIS method and its application in linguistic decision making

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Abstract Linguistic decision making is an important subject in decision making, many interesting and important linguistic decision making methods have been proposed, in which, alternatives-criteria decision matrix are uniformly used to express linguistic assessments of alternatives provided by decision makers with respect to criteria. Alternatives-criteria decision matrixes have some limitations when we use them to distinguish distinct, partial unknown or hesitant linguistic decision making or carry out linguistic decision making in the huge amounts of decision information and alternatives. In this paper, we propose alternatives-linguistic terms decision matrix to represent linguistic assessments of alternatives, analyze advantages of the decision matrix in representing linguistic assessments and distinguishing distinct, partial unknown or hesitant linguistic decision making. To simple and fast fuse alternatives-linguistic terms decision matrixes, we further provide linguistic multiset or fuzzy linguistic multiset to represent linguistic assessments in alternatives-linguistic terms decision matrixes, analyze the function properties of the fuzzy linguistic multiset. Motivated by fuzzy multiset and the TOPSIS method, we develop the fuzzy linguistic multiset TOPSIS method for linguistic decision making, the method is mainly consisted of transformation, aggregation and exploitation phases. In transformation phase, linguistic assessments of alternatives are transformed into fuzzy linguistic multisets by using alternatives-linguistic terms decision matrixes. In aggregation phase, we use Union, Intersection and Sum operations of multisets to obtain the positive and negative ideal solutions of linguistic decision making, which are different with the positive and negative ideal solutions of the traditional TOPSIS method, in addition, we provide a pseudo-distance between two fuzzy linguistic multisets to fast fuse linguistic assessments of alternatives. In exploitation phase, we define a new closeness degree of alternative by using pseudo-distances between the alternative and the positive and negative ideal solutions, which can be used to obtain the set of most satisfying alternatives. We also design an algorithm to carry out linguistic decision making based on the proposed method. In cases study, we use two practical examples to illustrate the practicality of the proposed method and compare it with the symbolic aggregation-based method, the hesitant fuzzy linguistic TOPSIS method, the hesitant fuzzy linguistic VIKOR method and the probabilistic linguistic term sets TOPSIS method, results indicate that alternatives-linguistic terms decision matrix and fuzzy linguistic multiset are alternative, useful and flexible tools for linguistic decision method and the fuzzy linguistic multiset TOPSIS method is suitable to deal with partial unknown or hesitant linguistic decision making.
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paper_title: Project management by multimoora as an instrument for transition economies

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Abstract The countries of Central and Eastern Europe moved from a previously centrally planned economy to a modern transition economy with strong market aspects. This paper proposes project management as an answer to this transition. Traditional Cost‐Benefit analysis does not respond to this purpose. Indeed Cost‐Benefit analysis is only interested in one specific project and not in a competition between projects. In addition all goals (objectives) have to be translated into money terms, leading sometimes to immoral consequences. On the contrary Multi‐Objective Optimization takes care of different objectives, whereas the objectives keep their own units. However different methods exist for the application of Multi‐Objective Optimization. The authors tested them after their robustness resulting in seven necessary conditions. MOORA (Multi‐Objective Optimization by Ratio analysis) and MULTIMOORA (MOORA plus Full Multiplicative Form), assisted by Ameliorated Nominal Group and Delphi Techniques, satisfy the seve...
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paper_title: Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment

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Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient's blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts' opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.
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paper_title: EXTENDED MULTIMOORA METHOD BASED ON SHANNON ENTROPY WEIGHT FOR MATERIALS SELECTION

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Selection of appropriate material is a crucial step in engineering design and manufacturing process. Without a systematic technique, many useful engineering materials may be ignored for selection. The category of multiple attribute decision-making (MADM) methods is an effective set of structured techniques. Having uncomplicated assumptions and mathematics, the MULTIMOORA method as an MADM approach can be effectively utilized for materials selection. In this paper, we developed an extension of MULTIMOORA method based on Shannon entropy concept to tackle materials selection process. The entropy concept was considered to assign relative importance to decision-making attributes. The proposed model consists of two scenarios named the weighted and entropy-weighted MULTIMOORA methods. In the first scenario, subjective weight was considered in the formulation of the approach like most of conventional MADM methods. The general form of entropy weight that is a combination of subjective and objective weighting factors was employed for the second scenario. We examined two popular practical examples concerning materials selection to show the application of the suggested approach and to reveal the effect of entropy weights. Our results were compared with the earlier studies.
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paper_title: Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA

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Abstract The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts’ cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript-based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods.
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paper_title: Robustness of MULTIMOORA: A Method for Multi-Objective Optimization

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Multi-Objective Optimization takes care of different objectives with the objectives keeping their own units. The internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred. The ratio system creates the opportunity to use a second approach: a Reference Point Theory, which uses the ratios of the ratio system. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added forming MULTIMOORA. The control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA, tested after robustness, showed positive results.
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paper_title: Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection

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A target-based MADM method covers beneficial and non-beneficial attributes besides target values for some attributes. Such techniques are considered as the comprehensive forms of MADM approaches. Target-based MADM methods can also be used in traditional decision-making problems in which beneficial and non-beneficial attributes only exist. In many practical selection problems, some attributes have given target values. The values of decision matrix and target-based attributes can be provided as intervals in some of such problems. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area of MADM techniques with target-based attributes under uncertainty of information. We extend the MULTIMOORA method for solving practical material selection problems in which material properties and their target values are given as interval numbers. We employ various concepts of interval computations to reduce degeneration of uncertain data. In this regard, we use interval arithmetic and introduce innovative formula for interval distance of interval numbers to create interval target-based normalization technique. Furthermore, we use a pairwise preference matrix based on the concept of degree of preference of interval numbers to calculate the maximum, minimum, and ranking of these numbers. Two decision-making problems regarding biomaterials selection of hip and knee prostheses are discussed. Preference degree-based ranking lists for subordinate parts of the extended MULTIMOORA method are generated by calculating the relative degrees of preference for the arranged assessment values of the biomaterials. The resultant rankings for the problem are compared with the outcomes of other target-based models in the literature.
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paper_title: Normalization and variant assessment methods in selection of road alignment variants – case study

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AbstractThe choice of the most beneficial road alignment variant is a multicriteria issue, based on transport, economic, social and environmental criteria. The criteria chosen for a multicriteria analysis can be expressed through measurable or immeasurable parameters. In order to compare and assess the variants it is necessary to normalize the criteria, which means a rescaling of their value, so that the criteria values fall into a specific range. The main aim of normalization is to assign an identical weight to each criterion in relation to other criteria. This article presents a review of the influence of criteria normalization methods and the variant assessment methods on the choice of the most beneficial road alignment variant on the example of the bypass of the town of Ksiezyno, which is a stretch of Regional Road 678 near Bialystok. Four variants of road alignment were compared and their ranking was created using six assessment methods. It was proven that the choices of the criteria normalization me...
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paper_title: Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications

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Abstract Materials selection as a significant step in engineering design process can be effectively implemented with the aid of MADM methods. The traditional MADM approaches only focus on beneficial or non-beneficial attributes to choose the optimal material; however, the selection should be made considering target values of attributes in some cases. In spite of practical applications of the target-based decision-making specially in engineering design problems, few studies have focused on the field. In the present paper, we developed a target-based MULTIMOORA method through introducing a normalization technique for materials selection in biomedical applications. We utilized two combinations of subjective, objective, and inter-attribute correlation effect significant coefficients to give importance to attributes. The information entropy and standard deviation concepts were used to assign two objective significant coefficients. This assumption leads to two modes of solution. Each mode has three subordinate and a final rankings. The final ranks of the two modes were consolidated into an aggregate ranking. The final and aggregate rankings were obtained using the dominance theory. We discussed two real-world biomedical engineering problems including materials selection for femoral components of hip and knee joint prostheses. Our aggregate rankings for the practical cases were compared with the results of previous studies.
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paper_title: Multi‐objective decision‐making for road design

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Abstract Multi‐objective analysis is a popular tool to solve many economic, managerial and construction problems. The objective of this research is to develop and implement a methodology for multi‐objective optimization of multi‐alternative decisions in road construction. After a rough overview of the articles dealing with the multi‐objective decision and assessment of road design alternatives described by discrete values, Multi‐Objective Optimization on the basis of the Ratio Analysis (MOORA) method was selected. This method focuses on a matrix of alternative responses on the objectives. A case study demonstrates the concept of multi‐objective optimization of road design alternatives and the best road design alternative is determined.
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paper_title: Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA

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Abstract The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts’ cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript-based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods.
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paper_title: Evaluation of excavator technologies: application of data fusion based MULTIMOORA methods

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Abstractexcavators are quite expensive vehicles. therefore, there may be huge losses for decision makers if a wrong decision is made during the purchasing process. A good evaluation of excavator alternatives both reduces costs and increases the benefits the excavator for the purchaser. The aim of this study is to prioritise excavator technologies to help decision makers during the purchasing process and to apply three different “data fusion methods” instead of the “theory of dominance” of the original MULTIMOORA method. the MULTIMOORA method is composed of three methods, namely: the ratio analysis as a part of MOORA, reference Point theory (the reference point approach as a part of MOORA) and the Full Multiplicative Form. it is used to prioritise excavator technologies in this study. the MULTIMOORA method combines three results obtained from these three methods using the theory of dominance. Dominance directed graph, rank position method and Borda count method as data fusion methods are also used to combi...
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paper_title: A De Novo multi-approaches multi-criteria decision making technique with an application in performance evaluation of material handling device

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We propose a De Novo MCDM model (TPOP) for precise ranking and selection.We introduce advanced version of entropy weighting method.This model (TPOP) eliminates inappropriate weights distribution.This model (TPOP) overcomes the rank reversal of the conventional approaches.The new model (TPOP) assists and guides decision makers. Application of multiple conventional approaches to a particular multi-criteria decision making (MCDM) problem often suffers rank reversal giving rise to confusion and ambiguity in appropriate decision making. To eradicate the confusion, this paper proposes a De Novo multi-approaches multi-criteria decision making method namely Technique of Precise Order Preference (TPOP). The TPOP first examines the inconsistency in the ranking order of the alternatives of a MCDM problem by using multiple conventional approaches. If inconsistency/rank reversal in ranking order of the alternatives exists then TPOP, using advanced version of entropy weighting method introduced in this research work, measures weights of the final selection values of conventional approaches. Subsequently, TPOP based on these weights and final selection values computes precise selection indices (PSI) that determines accurate ranking order for the alternatives. The proposed technique is illustrated by two real life examples on material handling device (MHD) ranking and selection problems. The first example is initially solved using five conventional integrated fuzzy multi-criteria decision making techniques (FMCDMs) whereas the second example is taken from previous researchers works. The results obtained using TPOP justify the validity, applicability and requirements of the proposed technique. The study shows that the proposed multi-approaches, multi-criteria decision making technique can be a useful and effective model in MCDM.
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paper_title: Robustness of MULTIMOORA: A Method for Multi-Objective Optimization

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Multi-Objective Optimization takes care of different objectives with the objectives keeping their own units. The internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred. The ratio system creates the opportunity to use a second approach: a Reference Point Theory, which uses the ratios of the ratio system. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added forming MULTIMOORA. The control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA, tested after robustness, showed positive results.
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paper_title: Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods

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Abstract In this paper, a novel decision methodology of critical path determination is introduced that not only considers project time but also considers project cost, risk, quality and safety. To address uncertain project environment, interval type-2 fuzzy sets (IT2FSs) are presented in the proposed decision methodology. The ratings of each activity and the weight of each criterion are described by IT2F-numbers. To address this multi-criteria decision problem, a new version of MULTIMOORA and MOOSRA methods are extended to IT2F-uncertainty and are used to determine project’s critical paths. In addition to addressing IT2FSs, the method is enhanced by replacing the commonly applied dominance theory by a new version of multi-approaches multi-criteria decision-making technique, namely technique of precise order preference (TPOP). Finally, in order to display the applicability of the presented methodology, an existing case study from the literature to aircraft prototype batch is adopted and solved. Furthermore, a case study of construction project is solved by proposed methodology. Also, sensitivity analysis and comparative analysis are carried out, and the results are discussed. The validity of the proposed methodology is confirmed by solving two decision methods of the recent literature. Furthermore, the sensitivity analysis illustrates that the critical path of the project is approximately insensitive to weights of new MULTIMOORA method's main parts.
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paper_title: A novel multi-attribute group decision-making method based on the MULTIMOORA with linguistic evaluations

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Multi-attribute group decision making (MAGDM) has been regarded as one of the most important branches in decision-making analysis. In the practical MAGDM problems, it is necessary to consider the connections among the different decision makers, as well as their trust levels. However, these issues are always neglected in the existing studies. In this paper, a novel method based on the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative From) is proposed to solve the MAGDM problems. Firstly, the weights of decision makers are determined based on the connections among different decision makers. Then, the linguistic evaluations are transformed into the form of triangular fuzzy numbers, and the normalized collective evaluations are determined, subsequently. In addition, based on the idea of classical MULTIMOORA method, the ranking result based on the ratio system, the reference point and the full multiplicative form are determined. Furthermore, an optimization model for determining the final ranking result is proposed, which has the minimum deviation with these three ranking results. Finally, an example concerning wastewater treatment is given to illustrate the feasibility and validity of the proposed method. The main contributions of this paper are: (i) the lengths of connections among these decision makers are utilized to determine the weights of different decision makers, (ii) the MULTIMOORA method is extended to solve the MAGDM problem with fuzzy linguistic evaluations and (iii) some desirable properties of the proposed method are discussed.
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paper_title: Probabilistic Linguistic MULTIMOORA: A Multicriteria Decision Making Method Based on the Probabilistic Linguistic Expectation Function and the Improved Borda Rule

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The probabilistic linguistic term set (PLTS) is a powerful technique in representing linguistic evaluations of individuals or groups in the process of decision making. The aim of this paper is to propose a strongly robust method to solve multiexperts multicriteria decision making problems with linguistic evaluations. To enrich the computation and to improve the measures of PLTS, we first define an expectation function of it. In addition, we advance three kinds of probabilistic linguistic distance measures reflecting on the difference of linguistic terms and probabilities at the same time to make up for the defects of the existing distance measures, and then propose the similarity and correlation measures. Integrating the subjective opinions with the correlation coefficients between criteria, we put forward a combined weight determining method. The robustness of the ranking method, MULTIMOORA, is enhanced by the improved Borda rule. Based on these research findings, a probabilistic linguistic MULTIMOORA method is proposed. Finally, the developed method is applied to an empirical example concerning the selection of shared karaoke television brands. The effectiveness of the proposed method is verified by some comparative analyses.
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paper_title: An improved MULTIMOORA approach for multi-criteria decision-making based on interdependent inputs of simplified neutrosophic linguistic information

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Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the flexibility and robustness it introduces into the decision process. This paper defines several simplified neutrosophic linguistic distance measures and employs a distance-based method to determine criterion weights. Then, an improved MULTIMOORA approach is presented by integrating the simplified neutrosophic linguistic normalized weighted Bonferroni mean and simplified neutrosophic linguistic normalized geometric weighted Bonferroni mean operators as well as a simplified neutrosophic linguistic distance measure. This approach ranks alternatives according to three ordering methods, and then, uses dominance theory to combine the three rankings into a single ranking. Finally, this paper presents a practical case example and conducts a comparative analysis between the proposed approach and existing methods in order to verify the feasibility and effectiveness of the developed methodology.
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paper_title: An Intuitionistic Multiplicative ORESTE Method for Patients’ Prioritization of Hospitalization

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The tension brought about by sickbeds is a common and intractable issue in public hospitals in China due to the large population. Assigning the order of hospitalization of patients is difficult because of complex patient information such as disease type, emergency degree, and severity. It is critical to rank the patients taking full account of various factors. However, most of the evaluation criteria for hospitalization are qualitative, and the classical ranking method cannot derive the detailed relations between patients based on these criteria. Motivated by this, a comprehensive multiple criteria decision making method named the intuitionistic multiplicative ORESTE (organisation, rangement et Synthese dedonnees relarionnelles, in French) was proposed to handle the problem. The subjective and objective weights of criteria were considered in the proposed method. To do so, first, considering the vagueness of human perceptions towards the alternatives, an intuitionistic multiplicative preference relation model is applied to represent the experts’ preferences over the pairwise alternatives with respect to the predetermined criteria. Then, a correlation coefficient-based weight determining method is developed to derive the objective weights of criteria. This method can overcome the biased results caused by highly-related criteria. Afterwards, we improved the general ranking method, ORESTE, by introducing a new score function which considers both the subjective and objective weights of criteria. An intuitionistic multiplicative ORESTE method was then developed and further highlighted by a case study concerning the patients’ prioritization.
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paper_title: Interpretation of criteria weights in multicriteria decision making

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Multicriteria decision making models are characterized by the need to evaluate a finite set of alternatives with respect to multiple criteria. The criteria weights in different aggregation rules have different interpretations and implications which have been misunderstood and neglected by many decision makers and researchers. By analyzing the aggregation rules, identifying partial values, specifying explicit measurement units and explicating direct statements of pairwise comparisons of preferences, we identify several plausible interpretations of criteria weights and their appropriate roles in different multicriteria decision making models. The underlying issues of scale validity, commensurability, criteria importance and rank consistency are examined.
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paper_title: The Recalculation of the Weights of Criteria in MCDM Methods Using the Bayes Approach

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The application of multiple criteria decision-making methods (MCDM) is aimed at choosing the best alternative out of the number of available versions in the absence of the apparently dominant alternative. One of the two major components of multiple criteria decision-making methods is represented by the weights of the criteria describing the considered process. The weights of the criteria quantitatively express their significance and influence on the evaluation result. The criterion weights can be subjective, i.e., based on the estimates assigned by the experts, and the so-called objective, i.e., those which assess the structure of the data array at the time of evaluation. Several groups of experts, representing the opinions of various interested parties may take part in the evaluation of criteria. The evaluation data on the criterion weights also depend on the mathematical methods used for calculations and the estimation scales. In determining the objective weights, several methods, assessing various properties or characteristics of the data array’s structure, are usually employed. Therefore, the use of the procedures, improving the accuracy of the evaluation of the weights’ values and the integration of the obtained data into a single value, is often required. The present paper offers a new approach to more accurate evaluation of the criteria weights obtained by using various methods based on the idea of the Bayes hypothesis. The performed investigation shows that the suggested method is symmetrical and does not depend on the fact whether a priori or posterior values of the weights are recalculated. This result is the theoretical basis for practical use of the method of combining the weights obtained by various approaches as the geometric mean of various estimates. The ideas suggested by the authors have been repeatedly used in the investigation for combining the objective weights, for recalculating the criteria weights after obtaining the estimates of other groups of experts and for combining the subjective and the objective weights. The recalculated values of the weights of the criteria are used in the work for evaluating the quality of the distant courses taught to the students.
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paper_title: A Theoretical Framework for Analysing the Notion of Relative Importance of Criteria

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Multiple-criteria decision aid almost always requires the use of weights, importance coefficients or even a hierarchy of criteria, veto thresholds, etc. These are importance parameters that are used to differentiate the role devoted to each criterion in the construction of comprehensive preferences. Many researchers have studied the problem of how to assign values to such parameters, but few of them have tried to analyse in detail what underlies the notion of importance of criteria and to give a clear formal definition of it. In this paper our purpose is to define a theoretical framework so as to analyse the notion of the importance of criteria under very general conditions. Within this framework it clearly appears that the importance of criteria is taken into account in very different ways in various aggregation procedures. This framework also allows us to shed new light on fundamental questions such as: Under what conditions is it possible to state that one criterion is more important than another? Are importance parameters of the various aggregation procedures dependent on or independent of the encoding of criteria? What are the links between the two concepts of the importance of criteria and the compensatoriness of preferences? This theoretical framework seems to us sufficiently general to ground further research in order to define theoretically valid elicitation methods for importance parameters.
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paper_title: ELECTRE: A comprehensive literature review on methodologies and applications

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Multi-criteria decision analysis (MCDA) is a valuable resource within operations research and management science. Various MCDA methods have been developed over the years and applied to decision problems in many different areas. The outranking approach, and in particular the family of ELECTRE methods, continues to be a popular research field within MCDA, despite its more than 40 years of existence. In this paper, a comprehensive literature review of English scholarly papers on ELECTRE and ELECTRE-based methods is performed. Our aim is to investigate how ELECTRE and ELECTRE-based methods have been considered in various areas. This includes area of applications, modifications to the methods, comparisons with other methods, and general studies of the ELECTRE methods. Although a significant amount of literature on ELECTRE is in a language different from English, we focus only on English articles, because many researchers may not be able to perform a study in some of the other languages. Each paper is categorized according to its main focus with respect to ELECTRE, i.e. if it considers an application, performs a review, considers ELECTRE with respect to the problem of selecting an MCDA method or considers some methodological aspects of ELECTRE. A total of 686 papers are included in the review. The group of papers considering an application of ELECTRE consists of 544 papers, and these are further categorized into 13 application areas and a number of sub-areas. In addition, all papers are classified according to the country of author affiliation, journal of publication, and year of publication. For the group of applied papers, the distribution by ELECTRE version vs. application area and ELECTRE version vs. year of publication are provided. We believe that this paper can be a valuable source of information for researchers and practitioners in the field of MCDA and ELECTRE in particular.
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paper_title: Robustness of MULTIMOORA: A Method for Multi-Objective Optimization

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Multi-Objective Optimization takes care of different objectives with the objectives keeping their own units. The internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred. The ratio system creates the opportunity to use a second approach: a Reference Point Theory, which uses the ratios of the ratio system. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added forming MULTIMOORA. The control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA, tested after robustness, showed positive results.
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paper_title: Panel building refurbishment elements effective selection by applying multiple-criteria methods

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Sustainable development has taken on a new concept: building maintenance, materials production, buildings demolition to determine the amount of energy and resources. This paper presents the process of effective selection of building elements for renovation which are important for energy effectiveness of buildings. Multi-criteria MOORA and MULTIMOORA methods has been adapt for problems solving with interval data. The paper presents a theoretical model of practice design renovation solutions evaluated. The theoretical model can also be applied to practical solutions to assess new construction planning stage, and other life-building processes.
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paper_title: Extension of MULTIMOORA method with interval numbers: An application in materials selection

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Abstract The MULTIMOORA method is developed using interval numbers based on fuzzy logic concept and a novel preference technique to deal with complex uncertain problems. By utilizing the fuzzy concept and considering relative weights for attributes, assessment values are obtained for subordinate parts of the interval weighted MULTIMOORA. We suggest an interval comparison matrix to calculate aggregate preference as an index to find the interval maximal objective reference point vector and rank the assessment values of the interval weighted ratio system and the full multiplicative form. The theory of dominance is employed to consolidate the subordinate ranks into the final ranking. Because of the reasonable assumption of alternative ratings as interval numbers in industrial problems and straightforward mathematics of the interval weighted MULTIMOORA, the proposed method can be effectively utilized by decision makers. A case study regarding materials selection of power gears is solved using the proposed method. Our final ranking for the practical case is verified with two interval-based and several crisp MADM methods.
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paper_title: Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection

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A target-based MADM method covers beneficial and non-beneficial attributes besides target values for some attributes. Such techniques are considered as the comprehensive forms of MADM approaches. Target-based MADM methods can also be used in traditional decision-making problems in which beneficial and non-beneficial attributes only exist. In many practical selection problems, some attributes have given target values. The values of decision matrix and target-based attributes can be provided as intervals in some of such problems. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area of MADM techniques with target-based attributes under uncertainty of information. We extend the MULTIMOORA method for solving practical material selection problems in which material properties and their target values are given as interval numbers. We employ various concepts of interval computations to reduce degeneration of uncertain data. In this regard, we use interval arithmetic and introduce innovative formula for interval distance of interval numbers to create interval target-based normalization technique. Furthermore, we use a pairwise preference matrix based on the concept of degree of preference of interval numbers to calculate the maximum, minimum, and ranking of these numbers. Two decision-making problems regarding biomaterials selection of hip and knee prostheses are discussed. Preference degree-based ranking lists for subordinate parts of the extended MULTIMOORA method are generated by calculating the relative degrees of preference for the arranged assessment values of the biomaterials. The resultant rankings for the problem are compared with the outcomes of other target-based models in the literature.
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paper_title: Interval target-based VIKOR method supported on interval distance and preference degree for machine selection

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By considering target values for attributes in addition to beneficial and non-beneficial attributes, a traditional MADM technique is converted to a comprehensive form. In many machine selection problems, some attributes have given target values. The target value regarding a machine attribute can be reported as a range of data. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area. For example, fuzzy axiomatic design approach presents a target-based decision-making supported on common area of membership functions of alternative ratings and target values of attributes. However, it has detects on finding a complete ranking because of probable infinite values of assessment index. Two target-based VIKOR models with interval data exist in the literature; however, the target values of attributes or ratings of alternatives on attributes are crisp numbers in the models and their formulations may have some limitations. The present paper tries to fill the gap by developing the VIKOR method with both interval target values of attributes and interval ratings of alternatives on attributes. Moreover, we attempt to utilize the power of interval computations to minimize degeneration of uncertain information. In this regard, we employ interval arithmetic and introduce a new normalization technique based on interval distance of interval numbers. We use a preference matrix to determine extremum and rank interval numbers. Two machine selection problems concerning punching equipment and continuous fluid bed tea dryer are solved employing the proposed method. Preference-degree-based ranking lists are formed by calculating the relative degrees of preference for the arranged assessment values of the candidate machines. The resultant rankings for the problems are compared with the results of fuzzy axiomatic design approach and the interval target-based MULTIMOORA method and its subordinate parts. We introduce a novel interval target-based VIKOR method.We propose a new normalization technique based on interval distance of interval numbers.We employ preference matrices and generate preference-degree-based ranking lists.We examine two machine selection problems using the proposed method.
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paper_title: Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment

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Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient's blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts' opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.
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paper_title: Fuzzy Multicriteria Decision-Making Methods: A Comparative Analysis

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Given a multicriteria decision-making problem, an obvious question emerges: Which method should be used to solve it? Although some efforts had been made, the question remains open. The aim of this contribution is to compare a set of multicriteria decision-making methods sharing three features: same fuzzy information as input data, the need of a data normalization procedure, and quite similar information processing. We analyze the rankings produced by fuzzy MULTIMOORA, fuzzy TOPSIS (with two normalizations), fuzzy VIKOR, and fuzzy WASPAS with different parameterizations, over 1200 randomly generated decision problems. The results clearly show their similarities and differences, the impact of the parameters settings, and how the methods can be clustered, thus providing some guidelines for their selection and usage.
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paper_title: Risk evaluation using a novel hybrid method based on FMEA, extended MULTIMOORA, and AHP methods under fuzzy environment

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Failure mode and effects analysis (FMEA) is one of the most important risk assessment tools which has been extensively used in different industries and organizations. In the conventional FMEA, sometimes the difference between some failure modes cannot be distinguished. In order to evaluate various failure modes more precisely, a novel fuzzy hybrid model for FMEA is proposed in this paper. In this method, fuzzy weighted risk priority number (FWRPN) is considered instead of RPN for each failure. The weights of the three factors and the weights of failure modes are computed by extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. The proposed fuzzy MULTIMOORA method calculates the weight of each failure based on three criteria of time, cost, and profit through fuzzy linguistic terms. After calculating FWRPN for each failure, corrective actions are performed for eliminating the identified failures or decreasing the effects of them. Then, corrected fuzzy weighted risk priority number (CFWRPN) is computed for each failure. Finally, the average of FWRPNs (AFWRPNs) with the average of CFWRPNs (ACFWRPNs) are compared to evaluate the effectiveness of corrective actions by a novel ranking fuzzy numbers method. In addition, the proposed ranking fuzzy number method is also used in both previously mentioned fuzzy multi-criteria decision making (MCDM) methods. Eventually, Kerman Steel Industries Factory is considered as a case study to demonstrate the applicability and benefits of the proposed fuzzy hybrid method. A sensitivity analysis is performed to validate the obtained results. Findings show that AFWRPNs decreased by 56% compared to ACFWRPNs.
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paper_title: Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method

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Multi criteria decision making (MCDM) often involves uncertainty which can be tackled by employing the fuzzy set theory. Type-2 fuzzy sets offer certain additional means for the latter purpose. This paper therefore extends the MULTIMOORA method with type-2 fuzzy sets viz. generalized interval-valued trapezoidal fuzzy numbers. The proposed method thus provides the means for multi-criteria decision making related to uncertain assessments. Utilization of aggregation operators also enables to facilitate group multi-criteria decision making. A numerical example of personnel selection demonstrates the possibilities of application of the proposed method in the field of human resource management and performance management in general.
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paper_title: Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment

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Failure mode and effect analysis (FMEA) is a prospective risk assessment tool used to identify, assess and eliminate potential failure modes in various industries to improve security and reliability. However, the conventional risk priority number (RPN) method has been widely criticized for the deficiencies in risk factor weights, calculation of RPN, evaluation of failure modes, etc. In this paper, we present a novel approach for FMEA based on interval-valued intuitionistic fuzzy sets (IVIFSs) and MULTIMOORA method to handle the uncertainty and vagueness from FMEA team members’ subjective assessments and to get a more accurate ranking of failure modes identified in FMEA. In this proposed model, interval-valued intuitionistic fuzzy (IVIF) continuous weighted entropy is applied for risk factor weighting and the IVIF-MULTIMOORA method is used to determine the risk priority order of failure modes. Finally, an illustrative case is provided to demonstrate the effectiveness and practicality of the proposed FMEA and a comparison analysis with other relevant methods is conducted to show its merits.
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paper_title: The Interval-Valued Intuitionistic Fuzzy MULTIMOORA Method for Group Decision Making in Engineering

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Multiple criteria decision making methods have received different extensions under the uncertain environment in recent years. The aim of the current research is to extend the application of the MULTIMOORA method (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form) for group decision making in the uncertain environment. Taking into account the advantages of IVIFS (interval-valued intuitionistic fuzzy sets) in handling the problem of uncertainty, the development of the interval-valued intuitionistic fuzzy MULTIMOORA (IVIF-MULTIMOORA) method for group decision making is considered in the paper. Two numerical examples of real-world civil engineering problems are presented, and ranking of the alternatives based on the suggested method is described. The results are then compared to the rankings yielded by some other methods of decision making with IVIF information. The comparison has shown the conformity of the proposed IVIF-MULTIMOORA method with other approaches. The proposed algorithm is favorable because of the abilities of IVIFS to be used for imagination of uncertainty and the MULTIMOORA method to consider three different viewpoints in analyzing engineering decision alternatives.
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paper_title: Use of IVFNs and MULTIMOORA method for supply chain performance measurement, benchmarking and decision-making: an empirical study

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In today’s competitive global marketplace, supply chain management (SCM) has become a key strategic consideration for achieving the organisational goals. The performance measurement of the entire supply chain is an important issue because it allows for tracking of efficacy and efficiency failures and leads to more informed decision-making with regard to chain design. Performance measurement is important as it affects behaviour that impacts supply chain performance. As such, performance measurement provides the means by which a company can assess whether its supply chain has improved or degraded. To this end, the present research aims to develop an efficient evaluation framework for selecting the best supply chain performance alternative from available alternatives. In this study, a fuzzy multi-criteria decision-making (FMADM) combined with multi-objective optimisation by ratio analysis (MULTIMOORA) has been explored towards appraisement and selection of the best supply chain in accordance with performance.
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paper_title: The multi-criteria hesitant fuzzy group decision making with MULTIMOORA method

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As a generalization of fuzzy set, hesitant fuzzy set permits the membership degree of an element to a set being represented by several possible values and thus can be considered as a powerful tool to express uncertain information in the process of group decision making. The aim of this study is to present a multi-criteria decision making method, namely MULTIMOORA-HF, to tackle hesitant fuzzy information. Being an extension of the crisp MULTIMOORA method, the MULTIMOORA-HF is designed to facilitate group decision making with uncertain information. The proposed methods consists of the three parts—the Ratio System, the Reference Point, and the Full Multiplicative Form. The proposed method thus provides the means for multi-criteria decision making related to uncertain and complex assessments. Utilization of aggregation operators also enables to reduce subjectivity and bias in the group multi-criteria decision making. The numerical simulation exhibits the possibilities for application of the proposed method.
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paper_title: Hazardous Materials Warehouse Selection as a Multiple Criteria Decision making Problem

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Radioactive, toxic, smother, flammable, and explosive materials in solid, liquid or gas states which can negatively impact goods, organisms, and most importantly humans are called as “Hazardous Materials”. Hazardous material transportation and storage carry risk factors in addition to their other types of transportation operations. Furthermore, selection of a suitable warehouse becomes a problematic issue in which multiple criteria are evaluated as paying attention to risky circumstances. In this context, hazardous material warehouse selection is considered as a multiple criteria decision problem in our study. In particularly, for the explosives storage among other hazardous materials, necessary criteria are determined according to expert’s consultant. The determined criteria are weighted according to decision makers’ consultancy and the alternatives are evaluated by fuzzy MULTIMOORA under uncertainty throughout the decision making process in the study.. The proposed approach is discussed on a case study.
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paper_title: Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods

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Abstract In this paper, a novel decision methodology of critical path determination is introduced that not only considers project time but also considers project cost, risk, quality and safety. To address uncertain project environment, interval type-2 fuzzy sets (IT2FSs) are presented in the proposed decision methodology. The ratings of each activity and the weight of each criterion are described by IT2F-numbers. To address this multi-criteria decision problem, a new version of MULTIMOORA and MOOSRA methods are extended to IT2F-uncertainty and are used to determine project’s critical paths. In addition to addressing IT2FSs, the method is enhanced by replacing the commonly applied dominance theory by a new version of multi-approaches multi-criteria decision-making technique, namely technique of precise order preference (TPOP). Finally, in order to display the applicability of the presented methodology, an existing case study from the literature to aircraft prototype batch is adopted and solved. Furthermore, a case study of construction project is solved by proposed methodology. Also, sensitivity analysis and comparative analysis are carried out, and the results are discussed. The validity of the proposed methodology is confirmed by solving two decision methods of the recent literature. Furthermore, the sensitivity analysis illustrates that the critical path of the project is approximately insensitive to weights of new MULTIMOORA method's main parts.
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paper_title: A farming efficiency estimation model based on fuzzy multimoora

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The paper focuses on development and application of the multi-criteria decision making framework for estimation of farming efficiency across different farming types. In this study time series data from the Farming Accountancy Data Network were analyzed. The research covers the period of 2003–2010. Indeed, reaching an economic efficiency is the foremost objective of managerial economics. Therefore, it is important to identify certain types of farming which are the forerunners or laggards in terms of operation efficiency. The following tasks were set: 1) to discuss the fuzzy MULTIMOORA method; 2) to develop the indicator set for efficiency assessment; 3) to evaluate efficiency of different farming types. The applied fuzzy MULTIMOORA method enabled to tackle the uncertainty specific to economic phenomena. The results showed that the most efficient farming type was horticulture and permanent crop farming. The second most efficient farming type was mixed field crop – granivore, pig farming. Mixed cropping, field crops – grazing livestock, and mixed livestock, grazing were ranked as those below the average farm in terms of efficiency. These types of farming should receive the highest support for technological improvements. JEL codes: C440, Q100, Q130.
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paper_title: A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead time

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Apart from the supplier selection literature, we employed MULTIMOORA and integrated it with multi-objective linear programming (MOLP) model under fuzzy environment.We aimed to contribute to the literature by developing a fuzzy model to support managers' decision on multi-product problem by evaluating lead time and quantity discounts simultaneously.We demonstrated a real life case study to check the applicability of the model.We compared the findings from different methods and observed findings are consistent and robust with the suggested method. Supplier selection is one of the major determinants of organizational competitiveness. The decisions on supplier selection are inherently complicated because of the necessity to consider simultaneously a variety of conflicting issues in a broad set of criteria from strategic to operational, and from quantitative to qualitative. In this study we developed a two-stage fuzzy approach to supplier selection and order allocation problem. In the first stage, fuzzy MULTIMOORA was utilized to evaluate and select suppliers with regard to subjective measures. Then, in the second stage fuzzy goal programming was used to determine the amount of order allocated to selected suppliers. The problem is formulated as a multi-product, multi-supplier problem having multiple objectives by satisfying quantity discounts, lead time, capacity and demand constraints. We used augmented max-min model guaranteeing non-dominated solutions, to transform the fuzzy multiobjective model into a crisp single objective function model. The results of each stage were compared with those obtained from other alternative techniques. The study also covers a real life problem to test the applicability and feasibility of the approach.
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paper_title: Application of fuzzy integrated MULTIMOORA method towards supplier/partner selection in agile supply chain

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Today's more dynamic business environment increases the need for greater agility in supply chains, which increases both the importance and frequency of supplier/partner selection decision–making. The contribution of this paper is the development of a framework and a decision model for supplier/partner selection in agile supply chain by utilising a fuzzy logic integrated with MULTIMOORA method. This paper presents a host of metrics and measures from extant literature on agility, which has been utilised in the development of the appraisement framework and model. Empirical data has been analysed to exhibit application feasibility of the proposed approach.
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paper_title: Fuzzy entropy-weighted MULTIMOORA method for materials selection

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The selection of proper material is a formative stage in engineering design and production process. Without a systematic approach, many practical engineering materials may be neglected for selection. Multiple attribute decision making techniques as efficient methodologies can aid decision-makers in finding the optimal option. As a robust multiple attribute decision making approach, the MULTIMOORA method can be usefully employed in materials selection process. In this study, we extend the MULTIMOORA approach based on Shannon entropy concept under fuzzy environment to solve a materials selection case that is a group multiple attribute decision making problem. In the present paper, subjective weights of attributes and the ratings of alternatives on attributes are assumed as fuzzy sets. The entropy concept is considered to assign objective relative importance to decision-making attributes. The fuzzy subjective weights of attributes that are based on decision-makers comments and the crisp objective weights of attributes obtained using the entropy concept are consolidated to generate the fuzzy integrated entropy weights. We evaluate a practical materials selection problem related to automotive industry. We perform a sensitivity analysis by altering aggregation and normalization techniques besides the types of weighting. The materials rankings of the example are compared with the related study.
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paper_title: Personnel selection based on computing with words and fuzzy MULTIMOORA

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Personnel selection process is aimed at choosing the best candidate to fill the defined vacancy in a company. It determines the input quality of personnel and thus plays an important role in human resource management. Given the uncertain, ambiguous, and vague nature of personnel selection process, it requires the application of multi-criteria decision making (MCDM) methods for robust recruitment. This paper hence is aimed at extending the fuzzy MULTIMOORA for linguistic reasoning under group decision making. The fuzzy MULTIMOORA was further modified in this study. The fuzzy MULTIMOORA for group decision making (MULTIMOORA-FG) enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform more robust personnel selection procedures. A personnel selection problem illustrated the group decision-making procedure according to MULTIMOORA-FG: the enterprise has formed an executive committee consisting of four decision-makers to choose the best candidate from another four participants to fill the vacancy. The committee has decided to consider eight qualitative attributes expressed in linguistic variables. The numerical example exhibited possibilities for improvement of human resources management as well as any other business decision area by applying MULTIMOORA-FG.
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paper_title: Evaluating health-care waste treatment technologies using a hybrid multi-criteria decision making model

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Health-care waste (HCW) management is a high priority public health and environmental concern particularly in developing countries. The decision to select an optimal technology for the disposal of HCW is a complicated multi-criteria decision analysis problem involving both qualitative and quantitative factors. Evaluating HCW treatment technologies may be based on imprecise information or uncertain data. Moreover, there can be significant dependence and feedbacks between the different dimensions and criteria. However, most existing decision models for HCW cannot capture these complex interrelationships. In response, this paper proposes a novel hybrid multi-criteria decision making (MCDM) model by integrating the 2-tuple DEMATEL technique and fuzzy MULTIMOORA method for selection of HCW treatment alternatives. It makes use of modified 2-tuple DEMATEL for obtaining the relative weights of criteria and fuzzy MULTIMOORA for assessing the alternatives according to each criterion. Specifically, an empirical case in Shanghai, one of the largest cities in China, is provided to illustrate the potential of the new model. Results show that the proposed framework for evaluating HCW treatment technologies is effective and provides meaningful implications for engineering designers to refer.
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paper_title: A Historical Account of Types of Fuzzy Sets and Their Relationships

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In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.
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paper_title: A multi-phase QFD-based hybrid fuzzy MCDM approach for performance evaluation: A case of smart bike-sharing programs in Changsha

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Abstract The smart bike-sharing program (BSP), which is a novel bike-sharing mode of traditional BSP, has become popular in many cities in China. However, most BSP studies focus only on the socio-economic characteristics of the users, bike-sharing patterns, and impacts that influence bike-sharing demand. This study increases the knowledge on BSPs by presenting a hybrid fuzzy multi-criteria decision-making approach that is based on multi-phase quality function deployment. This approach covers the performance evaluation of smart BSPs allowing for customer voices under uncertain conditions. This method combines the fuzzy best-worst method (BWM), fuzzy maximizing deviation method (MDM), and fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA). It uses fuzzy BWM to determine priorities of customer requirements and company strategies and to obtain subjective importance coefficients of criteria. Fuzzy MDM is used to derive objective importance coefficients of criteria and fuzzy MULTIMOORA is used to rank alternatives in terms of each criterion. An empirical case in Changsha, which is one of the pilot areas for comprehensively supporting the reform for an environment-friendly and resource-conserving society ("two-oriented society") in China, is provided to illustrate the application of the proposed framework. Results can help enterprises and organizations improve their performance and provide high-quality products and services for customers.
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paper_title: MULTIMOORA-FG: A Multi-Objective Decision Making Method for Linguistic Reasoning with an Application to Personnel Selection

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This paper aims to extend fuzzy MULTIMOORA with linguistic reasoning and group decision-making (MULTIMOORA-FG). The new method consists of the three parts, namely the fuzzy Ratio System, the fuzzy Utopian Reference Point, and the fuzzy Full Multiplicative Form offering a robust comparison of alternatives against multiple objectives. In addition, MULTIMOORA-FG is designed to deal with triangular fuzzy numbers which, in turn, can resemble linguistic variables. MULTIMOORA-FG is a proper instrument for linguistic reasoning under fuzzy environment. In our study an application of personnel selection illustrates the group decision-making procedure according to MULTIMOORA-FG. Given the uncertainties peculiar of personnel selection, the application of multi-objective decision making (MODM) is required in this area. Fuzzy MULTIMOORA enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform a more robust personnel selection. The committee decided to consider eight qualitative characteristics expressed in linguistic variables. A numerical example exhibited possibilities for improvement of human resources management or any other business decision-making by applying MULTIMOORA-FG.
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paper_title: Green supplier selection in fuzzy context: a decision-making scenario on application of fuzzy-MULTIMOORA

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Green supply chain management has become an important avenue in current business scenario. The concept of GSCM is to integrate environmental thinking into traditional supply chain management. A firm's sustainability performance is greatly influenced by appropriate supplier selection in the green supply chain context. In selecting appropriate green supplier, various green criteria need to be considered along with traditional supplier selection criteria. The decision making in the context of green supplier selection becomes much more complex due to involvement of subjective selection criteria. Subjective human judgment often bears ambiguity and vagueness in the decision making; whilst fuzzy set theory overcomes the challenges of imprecise and inconsistent human judgment in ambiguous decision environment. In this context, a decision making scenario in relation to green supplier selection has been articulated in this paper aiming to investigate the applicability of MULTIMOORA in fuzzy setting (F-MULTIMOORA). The ranking order of candidate suppliers has been compared to that of fuzzy-TOPSIS. Finally, an attempt has been made to determine a unique quantitative performance index for each of the green suppliers; based on which a ranking order has also been arrived.
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paper_title: Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment

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Failure mode and effects analysis (FMEA) is a prospective risk assessment tool which has been widely used within various industries, particularly the aerospace, automotive and healthcare industries. However, the conventional risk priority number (RPN) method has been criticized much for its deficiencies in risk factor weights, computation of RPN, evaluation of failure modes and so on. Therefore ranking of failure modes based on their related risk factors is necessary seeking to overcome the shortcomings and enhance the assessment capability of the traditional FMEA. In this paper, we treat the risk factors and their weights as fuzzy variables and evaluate them using fuzzy linguistic terms. As a result, a new risk priority model is proposed for evaluating the risk of failure modes based on fuzzy set theory and MULTIMOORA method. An empirical case of preventing infant abduction is provided to illustrate the potential applications and benefits of the proposed fuzzy FMEA. The main findings of this article are related with the proposed technique for failure modes assessment and ranking, and application of this technique for the prevention of infant abduction, which is a devastating problem for a healthcare facility. A new FMEA model is developed by using fuzzy set theory and MULTIMOORA method.Risk factors and their weights are evaluated using fuzzy linguistic variables.Extended MULTIMOORA is used to determine the risk priority of failure modes.The proposed fuzzy FMEA can be a useful tool for failure modes assessment and ranking.
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paper_title: Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA

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Abstract The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts’ cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript-based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods.
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paper_title: Linguistic Decision Making: Theory and Methods

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This book provides a systematic introduction to linguistic aggregation operators, linguistic preference relations, and various models and approaches to multi-attribute decision making with linguistic information. Offers practical examples, tables and figures.
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paper_title: Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures

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We define the double hierarchy linguistic term set (DHLTS).We propose the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS).We establish some operational laws and properties of the DHHFLTS.We develop a MULTIMOORA method on the basis of DHHFLTS.We apply this MULTIMOORA method to deal with a practical decision making problem. In recent years, hesitant fuzzy linguistic term sets (HFLTSs) have been studied by many scholars and are becoming gradually mature. However, some shortcomings of HFLTS also emerged. To describe the complex linguistic terms or linguistic term sets more accurately and reasonably, in this paper, we introduce the novel concepts named double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). The operational laws and properties of the DHHFLTSs are developed as well.Afterwards, we investigate the multiple criteria decision making model with double hierarchy hesitant fuzzy linguistic information. We develop a double hierarchy hesitant fuzzy linguistic MULTIMOORA (DHHFL-MULTIMOORA) method to solve it. Furthermore, we apply the DHHFL-MULTIMOORA method to deal with a practical case about selecting the optimal city in China by evaluating the implementation status of haze controlling measures. Some comparisons between the DHHFL-MULTIMOORA method and the hesitant fuzzy linguistic TOPSIS method are provided to show the advantages of the proposed method.
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paper_title: 2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection

paper_content:

Purpose – The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment. Design/methodology/approach – The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (...
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paper_title: Power Battery Recycling Mode Selection Using an Extended MULTIMOORA Method

paper_content:

In order to improve the efficiency of the recycling of the electric vehicle power batteries and reduce the recycling cost, it is of great importance to select an optimal power battery recycling mode. In this paper, an extended MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus full Multiplicative form) approach which combines with the two-dimension uncertain linguistic variables (TDULVs) and the regret theory, called TDUL-RT-MULTIMOORA method, is developed for solving the power battery recycling mode decision-making (PBRMDM) problem. Firstly, the evaluations of the power battery recycling modes over criteria are given by the experts using the TDULVs, and the evaluations of all experts are aggregated into a group linguistic decision matrix by the TDULDWA operator. On the basis of the regret theory, the perceived utility decision matrix is constructed. And then, in order to avoid the disadvantages of the subjective weighting methods, such as the deviation from the measured data and the dependence on the experience and knowledge of the experts, an objective entropy weighting method is applied. After that, the MULTIMOORA method is introduced to rank the power battery recycling modes. In the end, an illustrative example is given to verify the effectiveness and practicability of the proposed method.
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paper_title: Robot Evaluation and Selection Using the Hesitant Fuzzy Linguistic MULTIMOORA Method

paper_content:

With the development of modern technology, industrial robots have been applied extensively in different industries to perform high-risk jobs and produce high-quality products. However, selecting an appropriate robot for a specific manufacturing environment is a difficult task for decision makers because of the increase in complexity, production demands, and the availability of different robot types. Normally, robot selection can be regarded as a complex multicriteria decision-making problem, and decision makers often use uncertain linguistic terms to express their assessments because of time pressure, lack of data, and their limited expertise. In this article, a modified MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus the Full Multiplicative Form) method based on hesitant fuzzy linguistic term sets (named HFL-MULTIMOORA) is proposed for evaluating and selecting the optimal robot for a given industrial application. This method deals with the decision makers’ uncertain assessments with hesitant fuzzy linguistic variables, which can increase the flexibility of representing linguistic information. Finally, an empirical example is presented to demonstrate the proposed method, and the results indicate that the HFL-MULTIMOORA provides a useful and practical tool for solving robot selection problems within a hesitant linguistic information environment.
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paper_title: Hesitant Fuzzy Linguistic Term Set and Its Application in Decision Making: A State-of-the-Art Survey

paper_content:

The hesitant fuzzy linguistic term set (HFLTS) has gained great success as it can be used to represent several linguistic terms or comparative linguistic expressions together with some context-free grammars. This new approach has enabled the analysis and computing of linguistic expressions with uncertainties and opened the door for the possibility to develop more comprehensive and powerful decision theories and methods based on linguistic knowledge. Lots of new approaches and proposals for decision-making problems have been proposed to overcome the limitations of previous linguistic decision-making approaches. Now and in the future, decision-making methodologies and algorithms with hesitant fuzzy linguistic models would be a quite promising research line representing a high-quality breakthrough in this topic. To facilitate the study on HFLTS theory, this paper makes a state-of-the-art survey on HFLTSs based on the 134 selected papers from Web of Sciences published from January 2012 to October 2017. We justify the motivation, definitions, operations, comparison methods and measures of HFLTSs. We also summarize the different extensions of HFLTSs. The studies on multiple criteria decision making (MCDM) with HFLTSs in terms of aggregation operators and MCDM methods are clearly reviewed. We also conduce some overviews on decision making with hesitant fuzzy linguistic preference relations. The applications, research challenges and future directions are also given.
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paper_title: An Integrated Multi-Criteria Decision Making Approach to Location Planning of Electric Vehicle Charging Stations

paper_content:

© 2000-2011 IEEE. Electric vehicles (EVs) are recognized as one of the most promising technologies worldwide to address the fossil fuel energy resource crisis and environmental pollution. As the initial work of EV charging station (EVCS) construction, site selection plays a vital role in its whole life cycle, which, however, is a complicated multiple criteria decision making (MCDM) problem involving many conflicting criteria. Therefore, this work aims to propose a novel integrated MCDM approach by a grey decision making trial and evaluation laboratory (DEMATEL) and uncertain linguistic multi-objective optimization by ratio analysis plus full multiplicative form (UL-MULTIMOORA) for determining the most suitable EVCS site in terms of multiple interrelated criteria. Specifically, the grey DEMATEL method is used to determine criteria weights and the UL-MULTIMOORA model is employed to evaluate and select the optimal site. Finally, an empirical example in Shanghai, China, is presented to demonstrate the applicability and effectiveness of the proposed approach. The results show that the proposed approach is a useful, practical, and effective way to find the optimal location of EVCSs.
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paper_title: Application of interval 2-tuple linguistic MULTIMOORA method for health-care waste treatment technology evaluation and selection.

paper_content:

The management of health-care waste (HCW) is a major challenge for municipalities, particularly in the cities of developing countries. Selection of the best treatment technology for HCW can be viewed as a complicated multi-criteria decision making (MCDM) problem which requires consideration of a number of alternatives and conflicting evaluation criteria. Additionally, decision makers often use different linguistic term sets to express their assessments because of their different backgrounds and preferences, some of which may be imprecise, uncertain and incomplete. In response, this paper proposes a modified MULTIMOORA method based on interval 2-tuple linguistic variables (named ITL-MULTIMOORA) for evaluating and selecting HCW treatment technologies. In particular, both subjective and objective importance coefficients of criteria are taken into consideration in the developed approach in order to conduct a more effective analysis. Finally, an empirical case study in Shanghai, the most crowded metropolis of China, is presented to demonstrate the proposed method, and results show that the proposed ITL-MULTIMOORA can solve the HCW treatment technology selection problem effectively under uncertain and incomplete information environment.
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paper_title: Probabilistic Linguistic MULTIMOORA: A Multicriteria Decision Making Method Based on the Probabilistic Linguistic Expectation Function and the Improved Borda Rule

paper_content:

The probabilistic linguistic term set (PLTS) is a powerful technique in representing linguistic evaluations of individuals or groups in the process of decision making. The aim of this paper is to propose a strongly robust method to solve multiexperts multicriteria decision making problems with linguistic evaluations. To enrich the computation and to improve the measures of PLTS, we first define an expectation function of it. In addition, we advance three kinds of probabilistic linguistic distance measures reflecting on the difference of linguistic terms and probabilities at the same time to make up for the defects of the existing distance measures, and then propose the similarity and correlation measures. Integrating the subjective opinions with the correlation coefficients between criteria, we put forward a combined weight determining method. The robustness of the ranking method, MULTIMOORA, is enhanced by the improved Borda rule. Based on these research findings, a probabilistic linguistic MULTIMOORA method is proposed. Finally, the developed method is applied to an empirical example concerning the selection of shared karaoke television brands. The effectiveness of the proposed method is verified by some comparative analyses.
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paper_title: Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach

paper_content:

Mining method selection (MMS) is one of the core contents in mining design. As the influencing factors of MMS are in general of ambiguity or uncertainty, MMS can therefore be deemed as a complex fuzzy multi-criteria decision making problem. To resolve this problem, an extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach is studied in this paper. Three major contributions of this study are included. At first, comparative importance is crisp number in most stepwise weight assessment ratio analysis (SWARA) method, while linguistic terms are utilized to determine the criteria weights in the improved SWARA. Then, several Heronian mean (HM) operators related to linguistic neutrosophic numbers (LNNs) are defined to cope with evaluating indicators’ interrelations. Special cases are discussed, and primary properties are proved as well. At last, in combination with improved SWARA and HM operators, a novel decision making method, extended MULTIMOORA approach based on LNNs, is proposed. Applying this new approach to selecting the optimal mining method through an example, the feasibility is indicated. In addition, analyses of the strengths of the presented method are performed in comparison with other existing approaches.
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paper_title: COTANGENT SIMILARITY MEASURE OF ROUGH NEUTROSOPHIC SETS AND ITS APPLICATION TO MEDICAL DIAGNOSIS

paper_content:

Similarity measure plays an important role in medical diagnosis. In this paper, a new rough cotangent similarity measure between two rough neutrosophic sets is proposed. The notion of rough neutrosophic set is used as vector representations in 3D-vector space. The rating of all elements in rough neutrosophic set is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsity- membership degree. A numerical example of the medical diagnosis is provided to show the effectiveness and flexibility of the proposed method.
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paper_title: Augmented reality goggles selection by using neutrosophic MULTIMOORA method

paper_content:

The purpose of this paper is to present the augmented reality (AR) eyeglass selection problem based on Neutrosophic MULTIMOORA method which is a very new multi-objective method.,The author evaluates five AR goggles according to six different criteria. Criteria have different weights and determined by analytic hierarchy process. The author used neutrosophic MULTIMOORA method in order to evaluate AR eyeglasses.,Five different AR eyeglasses were evaluated and the best one was selected according to six different criteria (benefit and non-benefit). According to Neutrosophic MULTIMOORA method, Sony AR eyeglass is selected as the best one. Neutrosophic MULTIMOORA method uses simple computational equations and it handles multi-objective decision making problems effectively.,Evaluating AR goggles by using the Neutrosophic MULTIMOORA method for the first time is the originality of this paper.
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paper_title: A Neutrosophic Extension of the MULTIMOORA Method

paper_content:

The aim of this manuscript is to propose a new extension of theMULTIMOORA method adapted for usage with a neutrosophic set. By using single valued neutrosophic sets, the MULTIMOORA method can be more efficient for solving complex problems whose solving requires assessment and prediction, i.e. those problems associated with inaccurate and unreliable data. The suitability of the proposed approach is presented through an example.
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paper_title: Model for residential house element and material selection by neutrosophic MULTIMOORA method

paper_content:

Abstract This article aims to create a theoretical evaluation model based on decision support methods for the residential house construction materials and elements selection. The research and analyses of most of the scientists are invoked on individual elements and materials of the building, which have an impact on different aspects of sustainability. Meanwhile, the integrated model covering all the key elements and materials of the single-family residential house has not been implemented. Thus, the problem of development of the general composite model of the element and material selection of single-family buildings is acute in many countries around the world. Our study assessed the specific technical parameters related to building materials: cost, thermal bridging, and load-bearing capacity, the outer material selection according to localisation, environmental performance, durability, weight. SWARA (Step-wise Weight Assessment Ratio Analysis) approach is applied to decision making to calculate the relative importance of the criteria. A single-valued neutrosophic set governs the proposed new extension of MULTIMOORA (Multiobjective Optimisation by Ratio Analysis Plus Full Multiplicative Form) method and allows to deal explicitly with the indeterminacy of the initial information. Our proposed new theoretical composite model for selection of elements, materials and other aspects of sustainability can be practically applied in creating the decision support system for the selection of single-family house elements and materials.
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paper_title: An improved MULTIMOORA approach for multi-criteria decision-making based on interdependent inputs of simplified neutrosophic linguistic information

paper_content:

Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the flexibility and robustness it introduces into the decision process. This paper defines several simplified neutrosophic linguistic distance measures and employs a distance-based method to determine criterion weights. Then, an improved MULTIMOORA approach is presented by integrating the simplified neutrosophic linguistic normalized weighted Bonferroni mean and simplified neutrosophic linguistic normalized geometric weighted Bonferroni mean operators as well as a simplified neutrosophic linguistic distance measure. This approach ranks alternatives according to three ordering methods, and then, uses dominance theory to combine the three rankings into a single ranking. Finally, this paper presents a practical case example and conducts a comparative analysis between the proposed approach and existing methods in order to verify the feasibility and effectiveness of the developed methodology.
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paper_title: ZBWM: The Z-number extension of Best Worst Method and its application for supplier development

paper_content:

Abstract Best Worst Method (BWM) has recently been proposed as a method for Multi Criteria Decision Making (MCDM). Studies show that BWM compared with other methods such as Analytic Hierarchy Process (AHP), leads to lower inconsistency of the results while reducing the number of required pairwise comparisons. MCDM methods such as BWM require accurate information. However, it often happens in practice that a level of uncertainty accompanies the information. The main aim of this paper is to address this problem and provide an integration of BWM and Z-numbers, namely ZBWM. Providing BWM with Z-numbers enables the BWM method to handle the uncertainty of information of a multi-criteria decision. Additionally, the capabilities of the proposed method in the process of utilizing the linguistic information dealing with big data are highlighted. The proposed method is examined to address a supplier development problem. By experimental results, we show that ZBWM results lower inconsistency when compared with BWM. A Z-number contains subjectivity in its fuzzy part, which can be addressed in future applications of ZBWM.
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paper_title: A Multicriteria Group Decision-Making Method Based on the Normal Cloud Model With Zadeh's Z -Numbers

paper_content:

Z -number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z -numbers under the condition that the weight information is completely unknown. Processing Z -numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z -number construct. First, the potential information involved in Z -numbers is invoked, and a novel concept of normal Z +-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z +-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.
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paper_title: A survey on rough set theory and its applications

paper_content:

Abstract After probability theory, fuzzy set theory and evidence theory, rough set theory is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge. In recent years, the research and applications on rough set theory have attracted more and more researchers' attention. And it is one of the hot issues in the artificial intelligence field. In this paper, the basic concepts, operations and characteristics on the rough set theory are introduced firstly, and then the extensions of rough set model, the situation of their applications, some application software and the key problems in applied research for the rough set theory are presented.
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paper_title: Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company

paper_content:

Supply chain presents a very complex field involving a large number of participants. The aim of the complete supply chain is finding an optimum from the aspect of all participants, which is a rather complex task. In order to ensure optimum satisfaction for all participants, it is necessary that the beginning phase consists of correct evaluations and supplier selection. In this study, the supplier selection was performed in the construction company, on the basis of a new approach in the field of multi-criteria model. Weight coefficients were obtained by DEMATEL (Decision Making Trial and Evaluation Laboratory) method, based on the rough numbers. Evaluation and the supplier selection were made on the basis of a new Rough EDAS (Evaluation based on Distance from Average Solution) method, which presents one of the latest methods in this field. In order to determine the stability of the model and the applicability of the proposed Rough EDAS method, an extension of the COPRAS and MULTIMOORA method by rough numbers was also performed in this study, and the findings of the comparative analysis were presented. Besides the new approaches based on the extension by rough numbers, the results are also compared with the Rough MABAC (MultiAttributive Border Approximation area Comparison) and Rough MAIRCA (MultiAttributive Ideal-Real Comparative Analysis). In addition, in the sensitivity analysis, 18 different scenarios were formed, the ones in which criteria change their original values. At the end of the sensitivity analysis, SCC (Spearman Correlation Coefficient) of the obtained ranges was carried out, confirming the applicability of the proposed approaches.
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paper_title: Rough sets theory

paper_content:

Abstract The basic concepts of the rough set theory are introduced and adequately illustrated. An example of the rough set theory application to the QSAR classification problem is presented. Numerous earlier applications of rough set theory to the various scientific domains suggest that it also can be a useful tool for the analysis of inexact, uncertain, or vague chemical data.
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paper_title: Panel building refurbishment elements effective selection by applying multiple-criteria methods

paper_content:

Sustainable development has taken on a new concept: building maintenance, materials production, buildings demolition to determine the amount of energy and resources. This paper presents the process of effective selection of building elements for renovation which are important for energy effectiveness of buildings. Multi-criteria MOORA and MULTIMOORA methods has been adapt for problems solving with interval data. The paper presents a theoretical model of practice design renovation solutions evaluated. The theoretical model can also be applied to practical solutions to assess new construction planning stage, and other life-building processes.
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paper_title: EXTENDED MULTIMOORA METHOD BASED ON SHANNON ENTROPY WEIGHT FOR MATERIALS SELECTION

paper_content:

Selection of appropriate material is a crucial step in engineering design and manufacturing process. Without a systematic technique, many useful engineering materials may be ignored for selection. The category of multiple attribute decision-making (MADM) methods is an effective set of structured techniques. Having uncomplicated assumptions and mathematics, the MULTIMOORA method as an MADM approach can be effectively utilized for materials selection. In this paper, we developed an extension of MULTIMOORA method based on Shannon entropy concept to tackle materials selection process. The entropy concept was considered to assign relative importance to decision-making attributes. The proposed model consists of two scenarios named the weighted and entropy-weighted MULTIMOORA methods. In the first scenario, subjective weight was considered in the formulation of the approach like most of conventional MADM methods. The general form of entropy weight that is a combination of subjective and objective weighting factors was employed for the second scenario. We examined two popular practical examples concerning materials selection to show the application of the suggested approach and to reveal the effect of entropy weights. Our results were compared with the earlier studies.
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paper_title: Risk evaluation using a novel hybrid method based on FMEA, extended MULTIMOORA, and AHP methods under fuzzy environment

paper_content:

Failure mode and effects analysis (FMEA) is one of the most important risk assessment tools which has been extensively used in different industries and organizations. In the conventional FMEA, sometimes the difference between some failure modes cannot be distinguished. In order to evaluate various failure modes more precisely, a novel fuzzy hybrid model for FMEA is proposed in this paper. In this method, fuzzy weighted risk priority number (FWRPN) is considered instead of RPN for each failure. The weights of the three factors and the weights of failure modes are computed by extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. The proposed fuzzy MULTIMOORA method calculates the weight of each failure based on three criteria of time, cost, and profit through fuzzy linguistic terms. After calculating FWRPN for each failure, corrective actions are performed for eliminating the identified failures or decreasing the effects of them. Then, corrected fuzzy weighted risk priority number (CFWRPN) is computed for each failure. Finally, the average of FWRPNs (AFWRPNs) with the average of CFWRPNs (ACFWRPNs) are compared to evaluate the effectiveness of corrective actions by a novel ranking fuzzy numbers method. In addition, the proposed ranking fuzzy number method is also used in both previously mentioned fuzzy multi-criteria decision making (MCDM) methods. Eventually, Kerman Steel Industries Factory is considered as a case study to demonstrate the applicability and benefits of the proposed fuzzy hybrid method. A sensitivity analysis is performed to validate the obtained results. Findings show that AFWRPNs decreased by 56% compared to ACFWRPNs.
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paper_title: Evaluation of excavator technologies: application of data fusion based MULTIMOORA methods

paper_content:

Abstractexcavators are quite expensive vehicles. therefore, there may be huge losses for decision makers if a wrong decision is made during the purchasing process. A good evaluation of excavator alternatives both reduces costs and increases the benefits the excavator for the purchaser. The aim of this study is to prioritise excavator technologies to help decision makers during the purchasing process and to apply three different “data fusion methods” instead of the “theory of dominance” of the original MULTIMOORA method. the MULTIMOORA method is composed of three methods, namely: the ratio analysis as a part of MOORA, reference Point theory (the reference point approach as a part of MOORA) and the Full Multiplicative Form. it is used to prioritise excavator technologies in this study. the MULTIMOORA method combines three results obtained from these three methods using the theory of dominance. Dominance directed graph, rank position method and Borda count method as data fusion methods are also used to combi...
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paper_title: Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment

paper_content:

Failure mode and effect analysis (FMEA) is a prospective risk assessment tool used to identify, assess and eliminate potential failure modes in various industries to improve security and reliability. However, the conventional risk priority number (RPN) method has been widely criticized for the deficiencies in risk factor weights, calculation of RPN, evaluation of failure modes, etc. In this paper, we present a novel approach for FMEA based on interval-valued intuitionistic fuzzy sets (IVIFSs) and MULTIMOORA method to handle the uncertainty and vagueness from FMEA team members’ subjective assessments and to get a more accurate ranking of failure modes identified in FMEA. In this proposed model, interval-valued intuitionistic fuzzy (IVIF) continuous weighted entropy is applied for risk factor weighting and the IVIF-MULTIMOORA method is used to determine the risk priority order of failure modes. Finally, an illustrative case is provided to demonstrate the effectiveness and practicality of the proposed FMEA and a comparison analysis with other relevant methods is conducted to show its merits.
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paper_title: Extension of MULTIMOORA method with interval numbers: An application in materials selection

paper_content:

Abstract The MULTIMOORA method is developed using interval numbers based on fuzzy logic concept and a novel preference technique to deal with complex uncertain problems. By utilizing the fuzzy concept and considering relative weights for attributes, assessment values are obtained for subordinate parts of the interval weighted MULTIMOORA. We suggest an interval comparison matrix to calculate aggregate preference as an index to find the interval maximal objective reference point vector and rank the assessment values of the interval weighted ratio system and the full multiplicative form. The theory of dominance is employed to consolidate the subordinate ranks into the final ranking. Because of the reasonable assumption of alternative ratings as interval numbers in industrial problems and straightforward mathematics of the interval weighted MULTIMOORA, the proposed method can be effectively utilized by decision makers. A case study regarding materials selection of power gears is solved using the proposed method. Our final ranking for the practical case is verified with two interval-based and several crisp MADM methods.
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paper_title: Selection of optimum design for conical segmented aluminum tubes as energy absorbers: Application of MULTIMOORA method

paper_content:

Abstract The optimum design for energy absorbers requires considering different criteria. Therefore, the design process can benefit from Multiple-Attribute Decision-Making (MADM) approach. Thin-walled structures can be particularly employed as energy absorbers in automobiles to dissipate energy and protect passengers from the peak crush load caused by severe collisions. The present study investigates a thin-walled conical segmented aluminum tube which consists of several circular sections with different thicknesses. To achieve the optimum design, a number of conical segmented tubes were modeled by finite element method. Energy absorption, initial peak load, crush force efficiency (the ratio of mean load to maximum load), mass of the structure and deformation type as the conflicting objective functions were defined as attributes/criteria. The numeric logic (NL) technique was applied to determine the weight of various criteria. Furthermore, the MULTIMOORA method, as a well-accepted MADM model, was utilized to obtain the optimum design for a conical segmented tube. The design variables included wall thickness, lengths of sections, and taper angle. Drawing a comparison between the top rank conical segmented tube and the top rank conical simple tube revealed that the conical segmented tube could increase the efficiency of the crush load up to 23.8% and reduce the initial peak load and mass of the tube up to 54% and 17.54%, respectively.
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paper_title: The Interval-Valued Intuitionistic Fuzzy MULTIMOORA Method for Group Decision Making in Engineering

paper_content:

Multiple criteria decision making methods have received different extensions under the uncertain environment in recent years. The aim of the current research is to extend the application of the MULTIMOORA method (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form) for group decision making in the uncertain environment. Taking into account the advantages of IVIFS (interval-valued intuitionistic fuzzy sets) in handling the problem of uncertainty, the development of the interval-valued intuitionistic fuzzy MULTIMOORA (IVIF-MULTIMOORA) method for group decision making is considered in the paper. Two numerical examples of real-world civil engineering problems are presented, and ranking of the alternatives based on the suggested method is described. The results are then compared to the rankings yielded by some other methods of decision making with IVIF information. The comparison has shown the conformity of the proposed IVIF-MULTIMOORA method with other approaches. The proposed algorithm is favorable because of the abilities of IVIFS to be used for imagination of uncertainty and the MULTIMOORA method to consider three different viewpoints in analyzing engineering decision alternatives.
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paper_title: Ranking Heating Losses in a Building by Applying the MULTIMOORA

paper_content:

Nowadays everyone likes a nation or a company until it tries to reduce energy losses in heating. This paper proposes the project to study energy losses in heating a building. Investigations and heating losses calculations were made and methods selected to optimize the results. These methods concern MOORA (Multi-Objective Optimization by Ratio analysis) and MULTIMOORA (MOORA plus Full Multiplicative Form). Starting with a matrix of alternative responses on the objectives, three approaches come to an unambiguous result.
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paper_title: Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach

paper_content:

Mining method selection (MMS) is one of the core contents in mining design. As the influencing factors of MMS are in general of ambiguity or uncertainty, MMS can therefore be deemed as a complex fuzzy multi-criteria decision making problem. To resolve this problem, an extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach is studied in this paper. Three major contributions of this study are included. At first, comparative importance is crisp number in most stepwise weight assessment ratio analysis (SWARA) method, while linguistic terms are utilized to determine the criteria weights in the improved SWARA. Then, several Heronian mean (HM) operators related to linguistic neutrosophic numbers (LNNs) are defined to cope with evaluating indicators’ interrelations. Special cases are discussed, and primary properties are proved as well. At last, in combination with improved SWARA and HM operators, a novel decision making method, extended MULTIMOORA approach based on LNNs, is proposed. Applying this new approach to selecting the optimal mining method through an example, the feasibility is indicated. In addition, analyses of the strengths of the presented method are performed in comparison with other existing approaches.
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paper_title: 2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection

paper_content:

Purpose – The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment. Design/methodology/approach – The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (...
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paper_title: Lithuanian case study of masonry buildings from the Soviet period

paper_content:

This paper presents the process of effective selection of building elements for renovation important for energy saving in buildings. A large part of energy is lost in non-effective buildings. Therefore, in renovation of buildings, it is important to select effective structural improvements. Building insulation could not only save energy but also time, money and materials, which means that different objectives expressed in different units have to be fulfilled. Although different methods exist for the application of Multi Objective Optimisation, MULTIMOORA, which is composed of three sub-methods – Ratio System, Reference Point Method that uses ratios from the ratio system, and the Full Multiplicative Form – was preferred. Consequently, different solutions for building envelope renovation were ranked by MULTIMOORA as applied for masonry buildings from the Soviet period.
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paper_title: Power Battery Recycling Mode Selection Using an Extended MULTIMOORA Method

paper_content:

In order to improve the efficiency of the recycling of the electric vehicle power batteries and reduce the recycling cost, it is of great importance to select an optimal power battery recycling mode. In this paper, an extended MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus full Multiplicative form) approach which combines with the two-dimension uncertain linguistic variables (TDULVs) and the regret theory, called TDUL-RT-MULTIMOORA method, is developed for solving the power battery recycling mode decision-making (PBRMDM) problem. Firstly, the evaluations of the power battery recycling modes over criteria are given by the experts using the TDULVs, and the evaluations of all experts are aggregated into a group linguistic decision matrix by the TDULDWA operator. On the basis of the regret theory, the perceived utility decision matrix is constructed. And then, in order to avoid the disadvantages of the subjective weighting methods, such as the deviation from the measured data and the dependence on the experience and knowledge of the experts, an objective entropy weighting method is applied. After that, the MULTIMOORA method is introduced to rank the power battery recycling modes. In the end, an illustrative example is given to verify the effectiveness and practicability of the proposed method.
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paper_title: Robot Evaluation and Selection Using the Hesitant Fuzzy Linguistic MULTIMOORA Method

paper_content:

With the development of modern technology, industrial robots have been applied extensively in different industries to perform high-risk jobs and produce high-quality products. However, selecting an appropriate robot for a specific manufacturing environment is a difficult task for decision makers because of the increase in complexity, production demands, and the availability of different robot types. Normally, robot selection can be regarded as a complex multicriteria decision-making problem, and decision makers often use uncertain linguistic terms to express their assessments because of time pressure, lack of data, and their limited expertise. In this article, a modified MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus the Full Multiplicative Form) method based on hesitant fuzzy linguistic term sets (named HFL-MULTIMOORA) is proposed for evaluating and selecting the optimal robot for a given industrial application. This method deals with the decision makers’ uncertain assessments with hesitant fuzzy linguistic variables, which can increase the flexibility of representing linguistic information. Finally, an empirical example is presented to demonstrate the proposed method, and the results indicate that the HFL-MULTIMOORA provides a useful and practical tool for solving robot selection problems within a hesitant linguistic information environment.
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paper_title: A decision support system for agricultural machines and equipment selection: A case study on olive harvester machines

paper_content:

Abstract Olive is considered as one of the most important and useful products, but the traditional harvesting methods are failing to fulfill the current need; therefore, it is crucial to make the olive harvesting mechanized. In order to expedite the olive harvesting mechanization process, the engineers have designed various machines and equipment, which have their own special advantages. Now, the main challenge is to select the best olive harvesting machine to develop and improve the economic conditions in agricultural field to maintain the food demand. In the present study, we intend to present a decision support system to aid decision-making about olive harvesting machines. To achieve this target, we evaluate six candidate machines with nine important criteria and classify them into three groups: beneficial, non-beneficial, and target-based criteria. For weighting the criteria, the best-worst method is applied, and because of having target criterion in the selection problem, the decision matrix is normalized by the target-based technique. Finally, using two proposed methods, target-based MULTIMOORA and WASPAS, we select the best harvesting machine. In addition, we employ dominance method to integrate the resultant rankings of harvesting machines.
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paper_title: Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods

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Abstract In this paper, a novel decision methodology of critical path determination is introduced that not only considers project time but also considers project cost, risk, quality and safety. To address uncertain project environment, interval type-2 fuzzy sets (IT2FSs) are presented in the proposed decision methodology. The ratings of each activity and the weight of each criterion are described by IT2F-numbers. To address this multi-criteria decision problem, a new version of MULTIMOORA and MOOSRA methods are extended to IT2F-uncertainty and are used to determine project’s critical paths. In addition to addressing IT2FSs, the method is enhanced by replacing the commonly applied dominance theory by a new version of multi-approaches multi-criteria decision-making technique, namely technique of precise order preference (TPOP). Finally, in order to display the applicability of the presented methodology, an existing case study from the literature to aircraft prototype batch is adopted and solved. Furthermore, a case study of construction project is solved by proposed methodology. Also, sensitivity analysis and comparative analysis are carried out, and the results are discussed. The validity of the proposed methodology is confirmed by solving two decision methods of the recent literature. Furthermore, the sensitivity analysis illustrates that the critical path of the project is approximately insensitive to weights of new MULTIMOORA method's main parts.
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paper_title: Interval target-based VIKOR method supported on interval distance and preference degree for machine selection

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By considering target values for attributes in addition to beneficial and non-beneficial attributes, a traditional MADM technique is converted to a comprehensive form. In many machine selection problems, some attributes have given target values. The target value regarding a machine attribute can be reported as a range of data. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area. For example, fuzzy axiomatic design approach presents a target-based decision-making supported on common area of membership functions of alternative ratings and target values of attributes. However, it has detects on finding a complete ranking because of probable infinite values of assessment index. Two target-based VIKOR models with interval data exist in the literature; however, the target values of attributes or ratings of alternatives on attributes are crisp numbers in the models and their formulations may have some limitations. The present paper tries to fill the gap by developing the VIKOR method with both interval target values of attributes and interval ratings of alternatives on attributes. Moreover, we attempt to utilize the power of interval computations to minimize degeneration of uncertain information. In this regard, we employ interval arithmetic and introduce a new normalization technique based on interval distance of interval numbers. We use a preference matrix to determine extremum and rank interval numbers. Two machine selection problems concerning punching equipment and continuous fluid bed tea dryer are solved employing the proposed method. Preference-degree-based ranking lists are formed by calculating the relative degrees of preference for the arranged assessment values of the candidate machines. The resultant rankings for the problems are compared with the results of fuzzy axiomatic design approach and the interval target-based MULTIMOORA method and its subordinate parts. We introduce a novel interval target-based VIKOR method.We propose a new normalization technique based on interval distance of interval numbers.We employ preference matrices and generate preference-degree-based ranking lists.We examine two machine selection problems using the proposed method.
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paper_title: The construction sector in twenty European countries during the recession 2008–2009 – country ranking by MULTIMOORA

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The recession 2008-2009 which influenced the World economy has set new challenges for the development of the European construction sector. In the years 2008--2009 a great number of countries faced serious production and employment breakdowns. The purpose of this paper is to analyze the construction sector from a macroeconomic point of view by comparing construction market variations appeared during the crisis in twenty European countries. Therefore statistical indicators of the construction sector were used and a multiobjective evaluation method under the name of MULTIMOORA was employed. However these traditional indicators of the construction sector deliver an incomplete definition of real situations within the sector as during the recession plenty of constructed buildings remained unsold. Therefore the authors of this article propose a rather complex comparison of construction indicators for different European countries. The case study provides the analysis and calculations performed with the help of the MULTIMOORA method. This method enables the evaluation of European countries in accordance with the investigated objectives and ranges them into different groups according to the objectives set for the construction sector.
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paper_title: A farming efficiency estimation model based on fuzzy multimoora

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The paper focuses on development and application of the multi-criteria decision making framework for estimation of farming efficiency across different farming types. In this study time series data from the Farming Accountancy Data Network were analyzed. The research covers the period of 2003–2010. Indeed, reaching an economic efficiency is the foremost objective of managerial economics. Therefore, it is important to identify certain types of farming which are the forerunners or laggards in terms of operation efficiency. The following tasks were set: 1) to discuss the fuzzy MULTIMOORA method; 2) to develop the indicator set for efficiency assessment; 3) to evaluate efficiency of different farming types. The applied fuzzy MULTIMOORA method enabled to tackle the uncertainty specific to economic phenomena. The results showed that the most efficient farming type was horticulture and permanent crop farming. The second most efficient farming type was mixed field crop – granivore, pig farming. Mixed cropping, field crops – grazing livestock, and mixed livestock, grazing were ranked as those below the average farm in terms of efficiency. These types of farming should receive the highest support for technological improvements. JEL codes: C440, Q100, Q130.
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paper_title: Multicriteria assessment of unfinished construction projects

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Possible ways for assessing completion of unfinished residential buildings to achieve appropriate construction project objectives are presented in the paper. The developed model enables an efficient assessment of unfinished projects in Vilnius, the capital of Lithuania. Unfinished building solutions, expressed through indicators, were selected and used to formulate a multicriteria task to be solved by combinations of methods AHP+ARAS, MOORA and MULTIMOORA. A computational model was created and adjusted for a simple and efficient assessment of the adequacy of investment projects in many areas of construction.
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paper_title: A two-stage fuzzy approach for supplier evaluation and order allocation problem with quantity discounts and lead time

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Apart from the supplier selection literature, we employed MULTIMOORA and integrated it with multi-objective linear programming (MOLP) model under fuzzy environment.We aimed to contribute to the literature by developing a fuzzy model to support managers' decision on multi-product problem by evaluating lead time and quantity discounts simultaneously.We demonstrated a real life case study to check the applicability of the model.We compared the findings from different methods and observed findings are consistent and robust with the suggested method. Supplier selection is one of the major determinants of organizational competitiveness. The decisions on supplier selection are inherently complicated because of the necessity to consider simultaneously a variety of conflicting issues in a broad set of criteria from strategic to operational, and from quantitative to qualitative. In this study we developed a two-stage fuzzy approach to supplier selection and order allocation problem. In the first stage, fuzzy MULTIMOORA was utilized to evaluate and select suppliers with regard to subjective measures. Then, in the second stage fuzzy goal programming was used to determine the amount of order allocated to selected suppliers. The problem is formulated as a multi-product, multi-supplier problem having multiple objectives by satisfying quantity discounts, lead time, capacity and demand constraints. We used augmented max-min model guaranteeing non-dominated solutions, to transform the fuzzy multiobjective model into a crisp single objective function model. The results of each stage were compared with those obtained from other alternative techniques. The study also covers a real life problem to test the applicability and feasibility of the approach.
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paper_title: An Integrated Multi-Criteria Decision Making Approach to Location Planning of Electric Vehicle Charging Stations

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© 2000-2011 IEEE. Electric vehicles (EVs) are recognized as one of the most promising technologies worldwide to address the fossil fuel energy resource crisis and environmental pollution. As the initial work of EV charging station (EVCS) construction, site selection plays a vital role in its whole life cycle, which, however, is a complicated multiple criteria decision making (MCDM) problem involving many conflicting criteria. Therefore, this work aims to propose a novel integrated MCDM approach by a grey decision making trial and evaluation laboratory (DEMATEL) and uncertain linguistic multi-objective optimization by ratio analysis plus full multiplicative form (UL-MULTIMOORA) for determining the most suitable EVCS site in terms of multiple interrelated criteria. Specifically, the grey DEMATEL method is used to determine criteria weights and the UL-MULTIMOORA model is employed to evaluate and select the optimal site. Finally, an empirical example in Shanghai, China, is presented to demonstrate the applicability and effectiveness of the proposed approach. The results show that the proposed approach is a useful, practical, and effective way to find the optimal location of EVCSs.
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paper_title: Combined Multi-Criteria Decision Making Approach Based On Macbeth And Multi-MOORA Methods

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Various Multi-Criteria Decision Making (MCDM) methods have been developed to support decision making process. The main aim of all MCDM methods is to obtain ranking of the alternatives and select the best one under conflicting criteria. In this paper, a combined MCDM approach is proposed based on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation TecHnique) and MULTI-MOORA (Multi Objective Optimization on the basis of Ratio Analysis) methods. In this combined approach, the weights of the criteria are determined with MACBETH method and then MULTI-MOORA method is used to obtain the final ranking of the alternatives. At the end of the paper, to illustrate the applicability of the proposed approach an application of the automobile selection of a marble company is also given.
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paper_title: Augmented reality goggles selection by using neutrosophic MULTIMOORA method

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The purpose of this paper is to present the augmented reality (AR) eyeglass selection problem based on Neutrosophic MULTIMOORA method which is a very new multi-objective method.,The author evaluates five AR goggles according to six different criteria. Criteria have different weights and determined by analytic hierarchy process. The author used neutrosophic MULTIMOORA method in order to evaluate AR eyeglasses.,Five different AR eyeglasses were evaluated and the best one was selected according to six different criteria (benefit and non-benefit). According to Neutrosophic MULTIMOORA method, Sony AR eyeglass is selected as the best one. Neutrosophic MULTIMOORA method uses simple computational equations and it handles multi-objective decision making problems effectively.,Evaluating AR goggles by using the Neutrosophic MULTIMOORA method for the first time is the originality of this paper.
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paper_title: Fuzzy entropy-weighted MULTIMOORA method for materials selection

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The selection of proper material is a formative stage in engineering design and production process. Without a systematic approach, many practical engineering materials may be neglected for selection. Multiple attribute decision making techniques as efficient methodologies can aid decision-makers in finding the optimal option. As a robust multiple attribute decision making approach, the MULTIMOORA method can be usefully employed in materials selection process. In this study, we extend the MULTIMOORA approach based on Shannon entropy concept under fuzzy environment to solve a materials selection case that is a group multiple attribute decision making problem. In the present paper, subjective weights of attributes and the ratings of alternatives on attributes are assumed as fuzzy sets. The entropy concept is considered to assign objective relative importance to decision-making attributes. The fuzzy subjective weights of attributes that are based on decision-makers comments and the crisp objective weights of attributes obtained using the entropy concept are consolidated to generate the fuzzy integrated entropy weights. We evaluate a practical materials selection problem related to automotive industry. We perform a sensitivity analysis by altering aggregation and normalization techniques besides the types of weighting. The materials rankings of the example are compared with the related study.
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paper_title: Probabilistic Linguistic MULTIMOORA: A Multicriteria Decision Making Method Based on the Probabilistic Linguistic Expectation Function and the Improved Borda Rule

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The probabilistic linguistic term set (PLTS) is a powerful technique in representing linguistic evaluations of individuals or groups in the process of decision making. The aim of this paper is to propose a strongly robust method to solve multiexperts multicriteria decision making problems with linguistic evaluations. To enrich the computation and to improve the measures of PLTS, we first define an expectation function of it. In addition, we advance three kinds of probabilistic linguistic distance measures reflecting on the difference of linguistic terms and probabilities at the same time to make up for the defects of the existing distance measures, and then propose the similarity and correlation measures. Integrating the subjective opinions with the correlation coefficients between criteria, we put forward a combined weight determining method. The robustness of the ranking method, MULTIMOORA, is enhanced by the improved Borda rule. Based on these research findings, a probabilistic linguistic MULTIMOORA method is proposed. Finally, the developed method is applied to an empirical example concerning the selection of shared karaoke television brands. The effectiveness of the proposed method is verified by some comparative analyses.
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paper_title: A Neutrosophic Extension of the MULTIMOORA Method

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The aim of this manuscript is to propose a new extension of theMULTIMOORA method adapted for usage with a neutrosophic set. By using single valued neutrosophic sets, the MULTIMOORA method can be more efficient for solving complex problems whose solving requires assessment and prediction, i.e. those problems associated with inaccurate and unreliable data. The suitability of the proposed approach is presented through an example.
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paper_title: Model for residential house element and material selection by neutrosophic MULTIMOORA method

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Abstract This article aims to create a theoretical evaluation model based on decision support methods for the residential house construction materials and elements selection. The research and analyses of most of the scientists are invoked on individual elements and materials of the building, which have an impact on different aspects of sustainability. Meanwhile, the integrated model covering all the key elements and materials of the single-family residential house has not been implemented. Thus, the problem of development of the general composite model of the element and material selection of single-family buildings is acute in many countries around the world. Our study assessed the specific technical parameters related to building materials: cost, thermal bridging, and load-bearing capacity, the outer material selection according to localisation, environmental performance, durability, weight. SWARA (Step-wise Weight Assessment Ratio Analysis) approach is applied to decision making to calculate the relative importance of the criteria. A single-valued neutrosophic set governs the proposed new extension of MULTIMOORA (Multiobjective Optimisation by Ratio Analysis Plus Full Multiplicative Form) method and allows to deal explicitly with the indeterminacy of the initial information. Our proposed new theoretical composite model for selection of elements, materials and other aspects of sustainability can be practically applied in creating the decision support system for the selection of single-family house elements and materials.
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paper_title: Novel Integrated Multi-Criteria Model for Supplier Selection: Case Study Construction Company

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Supply chain presents a very complex field involving a large number of participants. The aim of the complete supply chain is finding an optimum from the aspect of all participants, which is a rather complex task. In order to ensure optimum satisfaction for all participants, it is necessary that the beginning phase consists of correct evaluations and supplier selection. In this study, the supplier selection was performed in the construction company, on the basis of a new approach in the field of multi-criteria model. Weight coefficients were obtained by DEMATEL (Decision Making Trial and Evaluation Laboratory) method, based on the rough numbers. Evaluation and the supplier selection were made on the basis of a new Rough EDAS (Evaluation based on Distance from Average Solution) method, which presents one of the latest methods in this field. In order to determine the stability of the model and the applicability of the proposed Rough EDAS method, an extension of the COPRAS and MULTIMOORA method by rough numbers was also performed in this study, and the findings of the comparative analysis were presented. Besides the new approaches based on the extension by rough numbers, the results are also compared with the Rough MABAC (MultiAttributive Border Approximation area Comparison) and Rough MAIRCA (MultiAttributive Ideal-Real Comparative Analysis). In addition, in the sensitivity analysis, 18 different scenarios were formed, the ones in which criteria change their original values. At the end of the sensitivity analysis, SCC (Spearman Correlation Coefficient) of the obtained ranges was carried out, confirming the applicability of the proposed approaches.
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paper_title: An improved MULTIMOORA approach for multi-criteria decision-making based on interdependent inputs of simplified neutrosophic linguistic information

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Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the flexibility and robustness it introduces into the decision process. This paper defines several simplified neutrosophic linguistic distance measures and employs a distance-based method to determine criterion weights. Then, an improved MULTIMOORA approach is presented by integrating the simplified neutrosophic linguistic normalized weighted Bonferroni mean and simplified neutrosophic linguistic normalized geometric weighted Bonferroni mean operators as well as a simplified neutrosophic linguistic distance measure. This approach ranks alternatives according to three ordering methods, and then, uses dominance theory to combine the three rankings into a single ranking. Finally, this paper presents a practical case example and conducts a comparative analysis between the proposed approach and existing methods in order to verify the feasibility and effectiveness of the developed methodology.
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paper_title: Ranking of the Lithuanian Banks During the Recession of 2008-2009 by the MULTIMOORA Method

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(ProQuest: ... denotes formulae omitted.)1. IntroductionApplications of Multi-Objective Optimization in banking has already been done by some researchers in the Technical University of Crete. They use their own Multiple Optimal Decision Analysis method, under the name of UTA (Figueira et al., 2005; Zopounidis, Pardalos, 2010). UTA group of methods uses linear programming techniques for optimizing a utility function associated with the preferences of a decision-maker. Variations of UTA are UTADIS and M.H.DIS for classification of alternatives or banks into two classes: healthy or bankrupt banks or firms (Dimitras et al., 1999; Doumpos et al., 2002; Gaganis et al., 2006), or into three classes: acceptable or healthy banks or firms, uncertain and unacceptable banks or firms (Zopounidis & Doumpos, 1999, 2002). Ioannidis et al. (2010) use the same methods but they add a decision tree classification, Euclidean distance to the k-nearest neighbors and stacked generalization. A multi-objective research on client-based variables has been done by Ginevicius & Podvezko (2008).A categorization of banks comprising major types of objectives forms the basis of this paper. A selection is made on the basis of a classification approach, known as CAMEL. CAMEL is very popular with scholars that do research in the areas of banking. It is an abbreviation for Capital adequacy, Asset quality, Management quality, Earnings and Liquidity. This categorization is used by the American Federal Reserve, FDIC (deposit insurance) and the OCC, Office of the Comptroller of the Currency (Podviezko & Ginevicius, 2010). The categorization comprises major types of objectives representing stability of banks. The well known international rating agency, Moody's Investors Inc., uses CAMEL-based objectives (Fanger, 2007).It has also been applied by Bongini et al. (2002), Thomson (1991), Arena (2008), Ozkan-Gunay & Ozkan (2007), Ginevicius & Podviezko (2011). Wheelock & Wilson (2000) and Cole & Gunther (1995) found that CAMEL-based variables strongly correlate with bank failures. Hirtle & Lopez (1999) found that CAMELbased examination of banks contain valuable information on bank condition for a 612 month period.Contrary to the micro-economic approach of CAMEL, another stream of thought focuses on a rather macro-economic way of thinking. Let us recall that micro-economics concerns an individual person, a firm or a government as owner or shareholder of a firm or as a receiver of taxes. On the contrary, macro-economics concerns the general economic welfare in a welfare economy (Pigou, 1950). Gonzalez & Hermosillo (1999) cite as macro-economic factors: "cyclical output downturns, adverse terms of trade shocks, declines in asset prices, rising real interest rates, boom-bust cycles in inflation, credit expansion, losses of foreign exchange reserves and capital inflows". With the banking crises in Asian countries of 1996-97, Demirguc et al., (1998) and Hardy & Pazarbasioglu (1998) argue that these models missed these crises. We have not considered a macro-economic approach as the banks we investigate are registered in Lithuania and therefore are operating in the same macro-economic environment governed by the same Law on Banks (Seimas of the Republic of Lithuania, 2004) and the deposits made with these banks are insured by the same State Enterprise "Deposit and Investment Insurance". Therefore branches of foreign banks, namely Danske Bank A/S and Nordea Bank Finland Plc are excluded as they are only branches, operating under Danish or Finnish law, respectively. They are registered in Lithuania only as branches, not as separate banks.In this paper, Lithuanian banks, as defined above, are ranked for the recession years 2008-2009 using multi-objective optimization. 2007 is taken as base year as the later years were seriously biased. The years 2008 and 2009 were characterized by a severe recession largely due to sub-prime and bank crisis problems1. …
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paper_title: The Future of Facilities Management in Lithuania

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This article presents a facilities management sector analysis and future forecast for Lithuania. The analysis was made in two stages: in 2003 and 2016. Since 2003, the date of the previous research study on facilities management, many changes have occurred in the economy of Lithuania, due to its accession to the European Union on May 1, 2004. In particular, the facilities management sector changed from a non- tradable to an internationally tradable sector, accompanied by the entrance of firms working at the European Union level. This means that traditional firms would have a price level problem, solved either by assuming the fidelity of existing clients or by lowering the quality of their services. The Ameliorated Nominal Group Technique was applied in this study. In addition to comparisons, a multi-objective optimization method helped to obtain a ranking of effectiveness of the firms offering facilities management. Therefore, the MULTIMOORA method is preferred, given its superiority to other methods. The final ranking of preference for the facilities sector in Lithuania is presented in this article. The future of facilities management in Lithuania is outlined. The main conclusions of the article are based on research conducted.
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paper_title: Multimoora Optimization Used to Decide on a Bank Loan to Buy Property

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Abstract Different multiple objectives are expressed in different units, which makes optimization difficult. Therefore the internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred to Weights which are most of the time used to compare the different units. In addition, the ratio system creates the opportunity to use a second approach: a non-subjective Reference Point Theory. The two approaches form a control on each other. The choice of the objectives is even more non-subjective if the opinion of all stakeholders interested in the issue is involved by the use of the Ameliorated Nominal Group and Delphi Techniques. The overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added to MOORA under the name of MULTIMOORA. At that moment the control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA is used to decide upon a ...
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paper_title: Multi-objective decision making in macro- and micro-economics with application of the MULTIMOORA method

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MULTIMOORA, the most effective method to respond to normalisation and importance of different objectives, substitutes by dimensionless measurements the use of weights; avoids the Condorcet-Arrow paradox by starting from a decision matrix instead of comparison two by two and is composed of three methods controlling each other. The ratio system of MOORA goes for a ratio system with each response of an alternative on an objective compared to a positive denominator, representative for all alternatives concerning that objective, ending with a total of objectives to be maximised, the objectives to be minimised subtracted. The reference point approach is the second method in MOORA by applying the ratios found earlier and whereby a maximal objective reference point is chosen. Finally, the MULTIMOORA method adds a third method, the full multiplicative form: all elements per row in the decision matrix are multiplied. Applications in macro and micro economics illustrate the issue.
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paper_title: Multi-Objective Decision Making With A Large Number of Objectives. An Application For Europe 2020

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The European Union attempts to reach a growing and sustainable economy by 2020, a much more moderate target than the 2010 target of becoming the most competitive and dynamic knowledge-based economy in the world. This intention has to be supported by an adequate Optimization and Decision Support System, such as MULTIMOORA. MULTIMOORA is a quantitative method, comparing multiple objectives, expressed in different units. In opposition to similar methods, MULTIMOORA does not need normalization, being based on dimensionless measures. MULTIMOORA is composed of three approaches: Ratio System, Reference Point and Multiplicative Form Methods, all of the same importance and each controlling each other. Twenty two objectives characterize the EU-Countries economies as a preparation for 2020. Unless important structural Decision Making will change their international position, "which of these countries are the best prepared for 2020" can be concluded from this study on basis of Ordinal Dominance.
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paper_title: How to invest in Belgian shares by MULTIMOORA optimization

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Different multiple objectives expressed in different units make optimization difficult. Therefore, the internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred to weights, which are most of the time used to compare the different units. In addition, the ratio system creates the opportunity to use a second approach: a non-subjective Reference Point Theory. Therefore, the Reference Point Theory uses the ratios found in the ratio system as co-ordinates for the alternative solutions, which are then compared to a Maximal Objective Reference Point. The two approaches form a control on each other. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added, three methods assembled under the name of MULTIMOORA. At that moment, the control by three different approaches forms a guaranty for a solution being as non-subjective as possible. As to calculate the sum of three obtained ranks is not allowed, a theory of Ordinal Dominance is developed in order to remain in the ordinal sphere.MULTIMOORA is used to decide upon an investment in Belgian shares on basis of a ranking in the BEL20 Index.
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paper_title: Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA

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Abstract The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts’ cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript-based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods.
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paper_title: Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures

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We define the double hierarchy linguistic term set (DHLTS).We propose the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS).We establish some operational laws and properties of the DHHFLTS.We develop a MULTIMOORA method on the basis of DHHFLTS.We apply this MULTIMOORA method to deal with a practical decision making problem. In recent years, hesitant fuzzy linguistic term sets (HFLTSs) have been studied by many scholars and are becoming gradually mature. However, some shortcomings of HFLTS also emerged. To describe the complex linguistic terms or linguistic term sets more accurately and reasonably, in this paper, we introduce the novel concepts named double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). The operational laws and properties of the DHHFLTSs are developed as well.Afterwards, we investigate the multiple criteria decision making model with double hierarchy hesitant fuzzy linguistic information. We develop a double hierarchy hesitant fuzzy linguistic MULTIMOORA (DHHFL-MULTIMOORA) method to solve it. Furthermore, we apply the DHHFL-MULTIMOORA method to deal with a practical case about selecting the optimal city in China by evaluating the implementation status of haze controlling measures. Some comparisons between the DHHFL-MULTIMOORA method and the hesitant fuzzy linguistic TOPSIS method are provided to show the advantages of the proposed method.
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paper_title: A GIS-based MCDM Approach for the Evaluation of Bike-share Stations

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Abstract –Several benefits have contributed to the increasing popularity of bike-share systems in cities around the world. In addition to traffic congestion, environmental concerns are also compelling cities to seek more sustainable modes of transportation. A key factor in the efficacy of bike-share networks is the location of bike stations in relation to potential related criteria. Therefore, site suitability analysis for bike-share stations using quantitative methods is essential. This study attempted to evaluate the current status of bike-share stations in Karsiyaka, Izmir, and to locate future station sites by comparing them to existing stations. To do so, different multi-criteria decision-making methods were combined with a geographic information system (GIS) to address twelve conflicting criteria. Specifically, the analytic hierarchy process was applied to obtain criteria weights, and multi-objective optimization by ratio analysis was used to evaluate current and potential alternatives. Our study demonstrates the superiority of the suggested locations compared to the existing stations.
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paper_title: Hazardous Materials Warehouse Selection as a Multiple Criteria Decision making Problem

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Radioactive, toxic, smother, flammable, and explosive materials in solid, liquid or gas states which can negatively impact goods, organisms, and most importantly humans are called as “Hazardous Materials”. Hazardous material transportation and storage carry risk factors in addition to their other types of transportation operations. Furthermore, selection of a suitable warehouse becomes a problematic issue in which multiple criteria are evaluated as paying attention to risky circumstances. In this context, hazardous material warehouse selection is considered as a multiple criteria decision problem in our study. In particularly, for the explosives storage among other hazardous materials, necessary criteria are determined according to expert’s consultant. The determined criteria are weighted according to decision makers’ consultancy and the alternatives are evaluated by fuzzy MULTIMOORA under uncertainty throughout the decision making process in the study.. The proposed approach is discussed on a case study.
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paper_title: A Multicriteria Group Decision-Making Method Based on the Normal Cloud Model With Zadeh's Z -Numbers

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Z -number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z -numbers under the condition that the weight information is completely unknown. Processing Z -numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z -number construct. First, the potential information involved in Z -numbers is invoked, and a novel concept of normal Z +-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z +-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.
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paper_title: A novel multi-attribute group decision-making method based on the MULTIMOORA with linguistic evaluations

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Multi-attribute group decision making (MAGDM) has been regarded as one of the most important branches in decision-making analysis. In the practical MAGDM problems, it is necessary to consider the connections among the different decision makers, as well as their trust levels. However, these issues are always neglected in the existing studies. In this paper, a novel method based on the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative From) is proposed to solve the MAGDM problems. Firstly, the weights of decision makers are determined based on the connections among different decision makers. Then, the linguistic evaluations are transformed into the form of triangular fuzzy numbers, and the normalized collective evaluations are determined, subsequently. In addition, based on the idea of classical MULTIMOORA method, the ranking result based on the ratio system, the reference point and the full multiplicative form are determined. Furthermore, an optimization model for determining the final ranking result is proposed, which has the minimum deviation with these three ranking results. Finally, an example concerning wastewater treatment is given to illustrate the feasibility and validity of the proposed method. The main contributions of this paper are: (i) the lengths of connections among these decision makers are utilized to determine the weights of different decision makers, (ii) the MULTIMOORA method is extended to solve the MAGDM problem with fuzzy linguistic evaluations and (iii) some desirable properties of the proposed method are discussed.
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paper_title: A multi-phase QFD-based hybrid fuzzy MCDM approach for performance evaluation: A case of smart bike-sharing programs in Changsha

paper_content:

Abstract The smart bike-sharing program (BSP), which is a novel bike-sharing mode of traditional BSP, has become popular in many cities in China. However, most BSP studies focus only on the socio-economic characteristics of the users, bike-sharing patterns, and impacts that influence bike-sharing demand. This study increases the knowledge on BSPs by presenting a hybrid fuzzy multi-criteria decision-making approach that is based on multi-phase quality function deployment. This approach covers the performance evaluation of smart BSPs allowing for customer voices under uncertain conditions. This method combines the fuzzy best-worst method (BWM), fuzzy maximizing deviation method (MDM), and fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA). It uses fuzzy BWM to determine priorities of customer requirements and company strategies and to obtain subjective importance coefficients of criteria. Fuzzy MDM is used to derive objective importance coefficients of criteria and fuzzy MULTIMOORA is used to rank alternatives in terms of each criterion. An empirical case in Changsha, which is one of the pilot areas for comprehensively supporting the reform for an environment-friendly and resource-conserving society ("two-oriented society") in China, is provided to illustrate the application of the proposed framework. Results can help enterprises and organizations improve their performance and provide high-quality products and services for customers.
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paper_title: Green supplier selection in fuzzy context: a decision-making scenario on application of fuzzy-MULTIMOORA

paper_content:

Green supply chain management has become an important avenue in current business scenario. The concept of GSCM is to integrate environmental thinking into traditional supply chain management. A firm's sustainability performance is greatly influenced by appropriate supplier selection in the green supply chain context. In selecting appropriate green supplier, various green criteria need to be considered along with traditional supplier selection criteria. The decision making in the context of green supplier selection becomes much more complex due to involvement of subjective selection criteria. Subjective human judgment often bears ambiguity and vagueness in the decision making; whilst fuzzy set theory overcomes the challenges of imprecise and inconsistent human judgment in ambiguous decision environment. In this context, a decision making scenario in relation to green supplier selection has been articulated in this paper aiming to investigate the applicability of MULTIMOORA in fuzzy setting (F-MULTIMOORA). The ranking order of candidate suppliers has been compared to that of fuzzy-TOPSIS. Finally, an attempt has been made to determine a unique quantitative performance index for each of the green suppliers; based on which a ranking order has also been arrived.
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paper_title: Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment

paper_content:

Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient's blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts' opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.
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paper_title: Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method

paper_content:

Multi criteria decision making (MCDM) often involves uncertainty which can be tackled by employing the fuzzy set theory. Type-2 fuzzy sets offer certain additional means for the latter purpose. This paper therefore extends the MULTIMOORA method with type-2 fuzzy sets viz. generalized interval-valued trapezoidal fuzzy numbers. The proposed method thus provides the means for multi-criteria decision making related to uncertain assessments. Utilization of aggregation operators also enables to facilitate group multi-criteria decision making. A numerical example of personnel selection demonstrates the possibilities of application of the proposed method in the field of human resource management and performance management in general.
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paper_title: The multi-criteria hesitant fuzzy group decision making with MULTIMOORA method

paper_content:

As a generalization of fuzzy set, hesitant fuzzy set permits the membership degree of an element to a set being represented by several possible values and thus can be considered as a powerful tool to express uncertain information in the process of group decision making. The aim of this study is to present a multi-criteria decision making method, namely MULTIMOORA-HF, to tackle hesitant fuzzy information. Being an extension of the crisp MULTIMOORA method, the MULTIMOORA-HF is designed to facilitate group decision making with uncertain information. The proposed methods consists of the three parts—the Ratio System, the Reference Point, and the Full Multiplicative Form. The proposed method thus provides the means for multi-criteria decision making related to uncertain and complex assessments. Utilization of aggregation operators also enables to reduce subjectivity and bias in the group multi-criteria decision making. The numerical simulation exhibits the possibilities for application of the proposed method.
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paper_title: Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection

paper_content:

A target-based MADM method covers beneficial and non-beneficial attributes besides target values for some attributes. Such techniques are considered as the comprehensive forms of MADM approaches. Target-based MADM methods can also be used in traditional decision-making problems in which beneficial and non-beneficial attributes only exist. In many practical selection problems, some attributes have given target values. The values of decision matrix and target-based attributes can be provided as intervals in some of such problems. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area of MADM techniques with target-based attributes under uncertainty of information. We extend the MULTIMOORA method for solving practical material selection problems in which material properties and their target values are given as interval numbers. We employ various concepts of interval computations to reduce degeneration of uncertain data. In this regard, we use interval arithmetic and introduce innovative formula for interval distance of interval numbers to create interval target-based normalization technique. Furthermore, we use a pairwise preference matrix based on the concept of degree of preference of interval numbers to calculate the maximum, minimum, and ranking of these numbers. Two decision-making problems regarding biomaterials selection of hip and knee prostheses are discussed. Preference degree-based ranking lists for subordinate parts of the extended MULTIMOORA method are generated by calculating the relative degrees of preference for the arranged assessment values of the biomaterials. The resultant rankings for the problem are compared with the outcomes of other target-based models in the literature.
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paper_title: Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications

paper_content:

Abstract Materials selection as a significant step in engineering design process can be effectively implemented with the aid of MADM methods. The traditional MADM approaches only focus on beneficial or non-beneficial attributes to choose the optimal material; however, the selection should be made considering target values of attributes in some cases. In spite of practical applications of the target-based decision-making specially in engineering design problems, few studies have focused on the field. In the present paper, we developed a target-based MULTIMOORA method through introducing a normalization technique for materials selection in biomedical applications. We utilized two combinations of subjective, objective, and inter-attribute correlation effect significant coefficients to give importance to attributes. The information entropy and standard deviation concepts were used to assign two objective significant coefficients. This assumption leads to two modes of solution. Each mode has three subordinate and a final rankings. The final ranks of the two modes were consolidated into an aggregate ranking. The final and aggregate rankings were obtained using the dominance theory. We discussed two real-world biomedical engineering problems including materials selection for femoral components of hip and knee joint prostheses. Our aggregate rankings for the practical cases were compared with the results of previous studies.
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paper_title: Application of interval 2-tuple linguistic MULTIMOORA method for health-care waste treatment technology evaluation and selection.

paper_content:

The management of health-care waste (HCW) is a major challenge for municipalities, particularly in the cities of developing countries. Selection of the best treatment technology for HCW can be viewed as a complicated multi-criteria decision making (MCDM) problem which requires consideration of a number of alternatives and conflicting evaluation criteria. Additionally, decision makers often use different linguistic term sets to express their assessments because of their different backgrounds and preferences, some of which may be imprecise, uncertain and incomplete. In response, this paper proposes a modified MULTIMOORA method based on interval 2-tuple linguistic variables (named ITL-MULTIMOORA) for evaluating and selecting HCW treatment technologies. In particular, both subjective and objective importance coefficients of criteria are taken into consideration in the developed approach in order to conduct a more effective analysis. Finally, an empirical case study in Shanghai, the most crowded metropolis of China, is presented to demonstrate the proposed method, and results show that the proposed ITL-MULTIMOORA can solve the HCW treatment technology selection problem effectively under uncertain and incomplete information environment.
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paper_title: Evaluating health-care waste treatment technologies using a hybrid multi-criteria decision making model

paper_content:

Health-care waste (HCW) management is a high priority public health and environmental concern particularly in developing countries. The decision to select an optimal technology for the disposal of HCW is a complicated multi-criteria decision analysis problem involving both qualitative and quantitative factors. Evaluating HCW treatment technologies may be based on imprecise information or uncertain data. Moreover, there can be significant dependence and feedbacks between the different dimensions and criteria. However, most existing decision models for HCW cannot capture these complex interrelationships. In response, this paper proposes a novel hybrid multi-criteria decision making (MCDM) model by integrating the 2-tuple DEMATEL technique and fuzzy MULTIMOORA method for selection of HCW treatment alternatives. It makes use of modified 2-tuple DEMATEL for obtaining the relative weights of criteria and fuzzy MULTIMOORA for assessing the alternatives according to each criterion. Specifically, an empirical case in Shanghai, one of the largest cities in China, is provided to illustrate the potential of the new model. Results show that the proposed framework for evaluating HCW treatment technologies is effective and provides meaningful implications for engineering designers to refer.
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paper_title: Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment

paper_content:

Failure mode and effects analysis (FMEA) is a prospective risk assessment tool which has been widely used within various industries, particularly the aerospace, automotive and healthcare industries. However, the conventional risk priority number (RPN) method has been criticized much for its deficiencies in risk factor weights, computation of RPN, evaluation of failure modes and so on. Therefore ranking of failure modes based on their related risk factors is necessary seeking to overcome the shortcomings and enhance the assessment capability of the traditional FMEA. In this paper, we treat the risk factors and their weights as fuzzy variables and evaluate them using fuzzy linguistic terms. As a result, a new risk priority model is proposed for evaluating the risk of failure modes based on fuzzy set theory and MULTIMOORA method. An empirical case of preventing infant abduction is provided to illustrate the potential applications and benefits of the proposed fuzzy FMEA. The main findings of this article are related with the proposed technique for failure modes assessment and ranking, and application of this technique for the prevention of infant abduction, which is a devastating problem for a healthcare facility. A new FMEA model is developed by using fuzzy set theory and MULTIMOORA method.Risk factors and their weights are evaluated using fuzzy linguistic variables.Extended MULTIMOORA is used to determine the risk priority of failure modes.The proposed fuzzy FMEA can be a useful tool for failure modes assessment and ranking.
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paper_title: Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment

paper_content:

Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient's blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts' opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.
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paper_title: An assessment of voting system simulations

paper_content:

In applying the results of the social choice theory to voting procedures, the question arises as to how often the various anomalies can be expected to occur. Computer simulations and probability modeling are common approaches to address this problem. This article is an attempt to find out the robustness of the so-called impartial culture assumption. For this purpose, a major perturbation of the impartial culture assumption is first considered and, thereafter, the author focuses on a few minor modifications of the assumption. Copyright 1992 by Kluwer Academic Publishers
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paper_title: A comparison of Dodgson's method and Kemeny's rule

paper_content:

Abstract. In an election without a Condorcet winner, Dodgson's method is designed to find the candidate that is “closest” to being a Condorcet winner. Similarly, if the head-to-head elections among all candidates do not give a complete transitive ranking, then Kemeny's Rule finds the “closest” transitive ranking. This paper uses geometric techniques to compare Dodgson's and Kemeny's notions of closeness and explain how conflict can arise between the two methods.
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paper_title: A Combined Finite Element-Multiple Criteria Optimization Approach for Materials Selection of Gas Turbine Components

paper_content:

The design of critical components for aerospace applications involves a number of conflicting functional requirements: reducing fuel consumption, cost, and weight, while enhancing performance, operability and robustness. As several materials systems and concepts remain competitive, a new approach that couples finite element analysis (FEA) and established multicriteria optimization protocols is developed in this paper. To demonstrate the approach, a prototypical materials selection problem for gas turbine combustor liners is chosen. A set of high temperature materials systems consisting of superalloys and thermal barrier coatings is considered as candidates. A thermomechanical FEA model of the combustor liner is used to numerically predict the response of each material system candidate. The performance of each case is then characterized by considering the material cost, manufacturability, oxidation resistance, damping behavior, thermomechanical properties, and the FEA postprocessed parameters relating to fatigue and creep. Using the obtained performance values as design criteria, an ELECTRE multiple attribute decision-making (MADM) model is employed to rank and classify the alternatives. The optimization model is enhanced by incorporating the relative importance (weighting factors) of the selection criteria, which is determined by multiple designers via a group decision-making process. [DOI: 10.1115/1.4006461]
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paper_title: Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks

paper_content:

The Analytic Network Process.- Forecasting the Resurgence of the U.S. Economy in 2001: An Expert Judgement Approach.- An Analytic Network Process Model for Financial-Crisis Forecasting.- Outsourcing a Firm's Application Development Group.- ANWR: Artic National Wildlife Refuge, an ANP Validation Example.- The Ford Explorer Case.- Synthesis of Complex Criteria Decision Making: A Case Towards a Consensus Agreement for a Middle East Conflict Resolution.- U.S. Energy Security.- Stabilizing Social Security for the Long-Term.- When Shall Poland Enter the Euro Zone?.- The Conflict between China and Taiwan.- U.S. Response to North Korean Nuclear Threat.- Criteria for Evaluating Group Decision-Making Methods.- An Innovative Orders-of-Magnitude Approach to AHP-Based Multicriteria Decision Making: Prioritizing Divergent Intangible Humane Acts.- Sensitivity Analysis in the Analytic Hierarchy Process.
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paper_title: Contractor selection with Multi Criteria Decision Support tools

paper_content:

The selection of the most suitable contractor is crucial for the success of construction projects. An important task in contractor selection is to establish a set of decision criteria that can measure and judge the capabilities of contractors. Multiple Criteria Decision Support (MCDS) methods can be very useful to solve this problem. Several MCDS tools are used in the literature for this problem. In order to promote the usage of these methods a set of them are applied to a real problem. It is also aimed to present the relative performances, advantages and disadvantages of these methods.
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paper_title: A genetic algorithm-based artificial neural network model with TOPSIS approach to optimize the engine performance

paper_content:

ABSTRACTThis paper describes the application of an artificial neural network, genetic algorithm and analytic network process-technique for order preference by similarity to ideal solution for the s...
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paper_title: Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems

paper_content:

This paper introduces hesitant uncertain linguistic Z-numbers (HULZNs) based on Z-numbers and linguistic models. HULZNs can serve as a reliable tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. This paper focuses on the development of an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is incompletely known. Handling qualitative information requires the effective support of quantitative tools, after which the linguistic scale function is employed to deal with linguistic information. First, the operations and distance of HULZNs are defined. Then, two power aggregation operators for HULZNs are proposed. Subsequently, a new MCGDM approach is developed by incorporating the power aggregation operators and the VIKOR model. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and validity of the proposed method are further verified by sensitivity analysis and comparison with an existing method.
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paper_title: Atanassov's Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model

paper_content:

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attention in multicriteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds, as well as several new aggregation operators: the trapezium cloud weighted arithmetic averaging operator, the trapezium cloud ordered weighted arithmetic averaging operator, and the trapezium cloud hybrid arithmetic operator. Moreover, a method with Atanassov's interval-valued intuitionistic linguistic numbers (AIVILNs) based on trapezium clouds is presented, which can provide solutions to multicriteria group decision-making problems with Atanassov's interval-valued intuitionistic linguistic information. In this method, AIVILNs are first converted into trapezium clouds and aggregated by trapezium cloud aggregation operators. Then, the ranking of alternatives is determined by the possibility degree matrix of trapezium clouds. Finally, an illustrative example confirming the validity and feasibility of the proposed method is given.
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paper_title: Trapezium cloud TOPSIS method with interval-valued intuitionistic hesitant fuzzy linguistic information

paper_content:

In the present study, we propose a novel trapezium cloud-based TOPSIS (technique for order preference by similarity to ideal solution) method with interval-valued intuitionistic hesitant fuzzy linguistic (IVIHFL) information. We also propose a method to transform IVIHFL numbers into trapezium clouds. Novel weighted Hamming, Euclidean, and Hausdorff distance measures for trapezium clouds are also defined in the present study. Advantage of proposed TOPSIS method is that it includes characteristic of cloud model of handling both randomness and fuzziness of qualitative perceptions with linguistic information. To understand the methodology of proposed trapezium cloud-based TOPSIS with IVIHFL information, we include an example of decision-making in stock selection. Proposed method is also compared with an existing recent method. We also include a validity test to confirm the outperformance of the ranking to validate its out performance. The proposed trapezium cloud-based TOPSIS method incorporates uncertainty, hesitancy, and inconsistency using both qualitative and quantitative information; this makes the proposed method unique from other TOPSIS methods.
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paper_title: Interval-Valued Neutrosophic Soft Sets

paper_content:

In this chapter, the concepts of interval-valued neutrosophic sets (IVNS in short), interval-valued neutrosophic soft sets (IVNSS in short) and IVNSS relations (IVNSS-relations in short) are proposed. The basic properties of IVNS-, IVNSS-, and IVNSS-relations are also presented and discussed. Also various types of IVNSS-relations are presented. Finally, a solution to a decision-making problem using IVNSS-relation is presented.
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paper_title: Generalized interval neutrosophic rough sets and its application in multi-attribute decision making

paper_content:

Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues.
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paper_title: Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection

paper_content:

A target-based MADM method covers beneficial and non-beneficial attributes besides target values for some attributes. Such techniques are considered as the comprehensive forms of MADM approaches. Target-based MADM methods can also be used in traditional decision-making problems in which beneficial and non-beneficial attributes only exist. In many practical selection problems, some attributes have given target values. The values of decision matrix and target-based attributes can be provided as intervals in some of such problems. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area of MADM techniques with target-based attributes under uncertainty of information. We extend the MULTIMOORA method for solving practical material selection problems in which material properties and their target values are given as interval numbers. We employ various concepts of interval computations to reduce degeneration of uncertain data. In this regard, we use interval arithmetic and introduce innovative formula for interval distance of interval numbers to create interval target-based normalization technique. Furthermore, we use a pairwise preference matrix based on the concept of degree of preference of interval numbers to calculate the maximum, minimum, and ranking of these numbers. Two decision-making problems regarding biomaterials selection of hip and knee prostheses are discussed. Preference degree-based ranking lists for subordinate parts of the extended MULTIMOORA method are generated by calculating the relative degrees of preference for the arranged assessment values of the biomaterials. The resultant rankings for the problem are compared with the outcomes of other target-based models in the literature.
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paper_title: A decision support system for agricultural machines and equipment selection: A case study on olive harvester machines

paper_content:

Abstract Olive is considered as one of the most important and useful products, but the traditional harvesting methods are failing to fulfill the current need; therefore, it is crucial to make the olive harvesting mechanized. In order to expedite the olive harvesting mechanization process, the engineers have designed various machines and equipment, which have their own special advantages. Now, the main challenge is to select the best olive harvesting machine to develop and improve the economic conditions in agricultural field to maintain the food demand. In the present study, we intend to present a decision support system to aid decision-making about olive harvesting machines. To achieve this target, we evaluate six candidate machines with nine important criteria and classify them into three groups: beneficial, non-beneficial, and target-based criteria. For weighting the criteria, the best-worst method is applied, and because of having target criterion in the selection problem, the decision matrix is normalized by the target-based technique. Finally, using two proposed methods, target-based MULTIMOORA and WASPAS, we select the best harvesting machine. In addition, we employ dominance method to integrate the resultant rankings of harvesting machines.
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paper_title: Interval target-based VIKOR method supported on interval distance and preference degree for machine selection

paper_content:

By considering target values for attributes in addition to beneficial and non-beneficial attributes, a traditional MADM technique is converted to a comprehensive form. In many machine selection problems, some attributes have given target values. The target value regarding a machine attribute can be reported as a range of data. Some target-based decision-making methods have recently been developed; however, a research gap exists in the area. For example, fuzzy axiomatic design approach presents a target-based decision-making supported on common area of membership functions of alternative ratings and target values of attributes. However, it has detects on finding a complete ranking because of probable infinite values of assessment index. Two target-based VIKOR models with interval data exist in the literature; however, the target values of attributes or ratings of alternatives on attributes are crisp numbers in the models and their formulations may have some limitations. The present paper tries to fill the gap by developing the VIKOR method with both interval target values of attributes and interval ratings of alternatives on attributes. Moreover, we attempt to utilize the power of interval computations to minimize degeneration of uncertain information. In this regard, we employ interval arithmetic and introduce a new normalization technique based on interval distance of interval numbers. We use a preference matrix to determine extremum and rank interval numbers. Two machine selection problems concerning punching equipment and continuous fluid bed tea dryer are solved employing the proposed method. Preference-degree-based ranking lists are formed by calculating the relative degrees of preference for the arranged assessment values of the candidate machines. The resultant rankings for the problems are compared with the results of fuzzy axiomatic design approach and the interval target-based MULTIMOORA method and its subordinate parts. We introduce a novel interval target-based VIKOR method.We propose a new normalization technique based on interval distance of interval numbers.We employ preference matrices and generate preference-degree-based ranking lists.We examine two machine selection problems using the proposed method.
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paper_title: Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications

paper_content:

Abstract Materials selection as a significant step in engineering design process can be effectively implemented with the aid of MADM methods. The traditional MADM approaches only focus on beneficial or non-beneficial attributes to choose the optimal material; however, the selection should be made considering target values of attributes in some cases. In spite of practical applications of the target-based decision-making specially in engineering design problems, few studies have focused on the field. In the present paper, we developed a target-based MULTIMOORA method through introducing a normalization technique for materials selection in biomedical applications. We utilized two combinations of subjective, objective, and inter-attribute correlation effect significant coefficients to give importance to attributes. The information entropy and standard deviation concepts were used to assign two objective significant coefficients. This assumption leads to two modes of solution. Each mode has three subordinate and a final rankings. The final ranks of the two modes were consolidated into an aggregate ranking. The final and aggregate rankings were obtained using the dominance theory. We discussed two real-world biomedical engineering problems including materials selection for femoral components of hip and knee joint prostheses. Our aggregate rankings for the practical cases were compared with the results of previous studies.
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paper_title: Ranking of the Lithuanian Banks During the Recession of 2008-2009 by the MULTIMOORA Method

paper_content:

(ProQuest: ... denotes formulae omitted.)1. IntroductionApplications of Multi-Objective Optimization in banking has already been done by some researchers in the Technical University of Crete. They use their own Multiple Optimal Decision Analysis method, under the name of UTA (Figueira et al., 2005; Zopounidis, Pardalos, 2010). UTA group of methods uses linear programming techniques for optimizing a utility function associated with the preferences of a decision-maker. Variations of UTA are UTADIS and M.H.DIS for classification of alternatives or banks into two classes: healthy or bankrupt banks or firms (Dimitras et al., 1999; Doumpos et al., 2002; Gaganis et al., 2006), or into three classes: acceptable or healthy banks or firms, uncertain and unacceptable banks or firms (Zopounidis & Doumpos, 1999, 2002). Ioannidis et al. (2010) use the same methods but they add a decision tree classification, Euclidean distance to the k-nearest neighbors and stacked generalization. A multi-objective research on client-based variables has been done by Ginevicius & Podvezko (2008).A categorization of banks comprising major types of objectives forms the basis of this paper. A selection is made on the basis of a classification approach, known as CAMEL. CAMEL is very popular with scholars that do research in the areas of banking. It is an abbreviation for Capital adequacy, Asset quality, Management quality, Earnings and Liquidity. This categorization is used by the American Federal Reserve, FDIC (deposit insurance) and the OCC, Office of the Comptroller of the Currency (Podviezko & Ginevicius, 2010). The categorization comprises major types of objectives representing stability of banks. The well known international rating agency, Moody's Investors Inc., uses CAMEL-based objectives (Fanger, 2007).It has also been applied by Bongini et al. (2002), Thomson (1991), Arena (2008), Ozkan-Gunay & Ozkan (2007), Ginevicius & Podviezko (2011). Wheelock & Wilson (2000) and Cole & Gunther (1995) found that CAMEL-based variables strongly correlate with bank failures. Hirtle & Lopez (1999) found that CAMELbased examination of banks contain valuable information on bank condition for a 612 month period.Contrary to the micro-economic approach of CAMEL, another stream of thought focuses on a rather macro-economic way of thinking. Let us recall that micro-economics concerns an individual person, a firm or a government as owner or shareholder of a firm or as a receiver of taxes. On the contrary, macro-economics concerns the general economic welfare in a welfare economy (Pigou, 1950). Gonzalez & Hermosillo (1999) cite as macro-economic factors: "cyclical output downturns, adverse terms of trade shocks, declines in asset prices, rising real interest rates, boom-bust cycles in inflation, credit expansion, losses of foreign exchange reserves and capital inflows". With the banking crises in Asian countries of 1996-97, Demirguc et al., (1998) and Hardy & Pazarbasioglu (1998) argue that these models missed these crises. We have not considered a macro-economic approach as the banks we investigate are registered in Lithuania and therefore are operating in the same macro-economic environment governed by the same Law on Banks (Seimas of the Republic of Lithuania, 2004) and the deposits made with these banks are insured by the same State Enterprise "Deposit and Investment Insurance". Therefore branches of foreign banks, namely Danske Bank A/S and Nordea Bank Finland Plc are excluded as they are only branches, operating under Danish or Finnish law, respectively. They are registered in Lithuania only as branches, not as separate banks.In this paper, Lithuanian banks, as defined above, are ranked for the recession years 2008-2009 using multi-objective optimization. 2007 is taken as base year as the later years were seriously biased. The years 2008 and 2009 were characterized by a severe recession largely due to sub-prime and bank crisis problems1. …
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Title: An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges

Section 1: Introduction
Description 1: This section introduces Multi-Criteria Decision-Making (MCDM) approaches and highlights the categorization and significance of different MCDM methods, leading up to the introduction of MULTIMOORA.

Section 2: MULTIMOORA theory and robustness
Description 2: This section discusses the theoretical features and robustness of MULTIMOORA, providing a bibliometric analysis, subordinate ranking methods, ranking aggregation tools, weighting methods, group decision-making structures, combination with other models, and justifying the robustness of MULTIMOORA.

Section 3: Analysis of the developments of MULTIMOORA based on uncertainty theories
Description 3: This section discusses the extensions of MULTIMOORA supported by various uncertainty theories, categorizing and analyzing the mathematical features of these models, and evaluating the significance of different uncertainty sets.

Section 4: Analysis of the applications of MULTIMOORA
Description 4: This section presents and categorizes the applications of MULTIMOORA across different sectors, such as industries, economics, civil services, environmental policymaking, healthcare management, and information and communications technologies.

Section 5: Challenges to future studies on MULTIMOORA
Description 5: This section identifies and discusses the challenges for future research in the theory, developments, and applications of MULTIMOORA, providing guidance on issues related to subordinate ranking methods, ranking aggregation tools, weighting methods for criteria, group decision-making, combination with other models, uncertain developments, and practical applications.

Section 6: Conclusions
Description 6: This section provides a summary of the main points discussed in the overview, focusing on the significance, uncertain extensions, applications, and future challenges of MULTIMOORA.