An overview of intuitionistic linguistic fuzzy information aggregations and applications
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paper_title: Induced generalized intuitionistic fuzzy operators

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We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster-Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster-Shafer operators. Then we investigate their various properties and some of their special cases. Additionally, we apply the developed operators to financial decision making under intuitionistic fuzzy environments. Some extensions in interval-valued intuitionistic fuzzy situations are also pointed out.
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paper_title: Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making

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Abstract With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic uncertain linguistic variables, some new group decision making analysis methods are developed. Firstly, some operational laws, expected value and accuracy function of interval-valued intuitionistic uncertain linguistic variables are introduced. Then, an interval-valued intuitionistic uncertain linguistic weighted geometric average (IVIULWGA) operator and an interval-valued intuitionistic uncertain linguistic ordered weighted geometric (IVIULOWG) operator have been developed. Furthermore, some desirable properties of the IVIULWGA operator and the IVIULOWG operator, such as commutativity, idempotency and monotonicity, have been studied, and an interval-valued intuitionistic uncertain linguistic hybrid geometric (IVIULHG) operator which generalizes both the IVIULWGA operator and the IVIULOWG operator, was developed. Based on these operators, an approach to multiple attribute group decision making with interval-valued intuitionistic uncertain linguistic information has been proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

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Abstract In this paper, a novel method is proposed to support the process of solving multi-objective nonlinear programming problems subject to strict or flexible constraints. This method assumes that the practical problems are expressed in the form of geometric programming problems. Integrating the concept of intuitionistic fuzzy sets into the solving procedure, a rich structure is provided which can include the inevitable uncertainties into the model regarding different objectives and constraints. Another important feature of the proposed method is that it continuously interacts with the decision maker. Thus, the decision maker could learn about the problem, thereby a compromise solution satisfying his/hers preferences could be obtained. Further, a new two-step geometric programming approach is introduced to determine Pareto-optimal compromise solutions for the problems defined during different iterative steps. Employing the compensatory operator of “weighted geometric mean”, the first step concentrates on finding an intuitionistic fuzzy efficient compromise solution. In the cases where one or more intuitionistic fuzzy objectives are fully achieved, a second geometric programming model is developed to improve the resulting compromise solution. Otherwise, it is concluded that the resulting solution vectors simultaneously satisfy both of the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The models forming the proposed solving method are developed in a way such that, the posynomiality of the defined problem is not affected. This property is of great importance when solving nonlinear programming problems. A numerical example of multi-objective nonlinear programming problem is also used to provide a better understanding of the proposed solving method.
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paper_title: An extended TODIM method for multiple attribute group decision making based on intuitionistic uncertain linguistic variables

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The intuitionistic uncertain linguistic variables are the good tools to express the fuzzy information, and the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method can consider the bounded rationality of decision makers based on the prospect theory. However, the classical TODIM method can only process the multiple attribute decision making (MADM) problems where the attribute values take the form of crisp numbers. In this paper, we will extend the TODIM method to the multiple attribute group decision making (MAGDM) with intuitionistic uncertain linguistic information. Firstly, the definition, characteristics, expectation, comparison method and distance of intuitionistic uncertain linguistic variables are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MAGDM problems with intuitionistic uncertain linguistic variables, and its significant characteristic is that it can fully consider the decision makers' bounded rationality which is a real action in decision making. Finally, an illustrative example is proposed to verify the developed approach.
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paper_title: Factorial-Quality Scalar and an Extension of ELECTRE in Intuitionistic Fuzzy Sets

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A great number of real-world problems can be associated with multi-criteria decision-making. These problems are often characterized by a high degree of uncertainty. Intuitionistic fuzzy sets (IFSs) are a generalized form of an ordinal fuzzy set to deal with this natural uncertainty. In this paper, we propose a hybrid version of the intuitionistic fuzzy ELECTRE based on VIKOR method, which was never considered before. The advantage and strengths of the intuitionistic fuzzy ELECTRE based on VIKOR method as decision aid technique and IFS as an uncertain framework make the proposed method a suitable choice in solving practical problems. Finally, a numerical example for engineering manager choice is given to illustrate the application of proposed method. The paper also gives a special view of point to the research along IFSs: It can be viewed as a kind of factorial scalar theory in factor space, which helps the authors to complete the paper with clear ideas.
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paper_title: Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making

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With respect to multiple attribute group decision making problems with linguistic information, some new decision analysis methods are proposed. Firstly, we develop three new aggregation operators: generalized 2-tuple weighted average (G-2TWA) operator, generalized 2-tuple ordered weighted average (G-2TOWA) operator and induced generalized 2-tuple ordered weighted average (IG-2TOWA) operator. Then, a method based on the IG-2TOWA and G-2TWA operators for multiple attribute group decision making is presented. In this approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.
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paper_title: Intuitionistic Fuzzy Aggregation Operators

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An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
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paper_title: New Divergence and Entropy Measures for Intuitionistic Fuzzy Sets on Edge Detection

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Edges of the image play an important role in the field of digital image processing and computer vision. The edges reduce the amount of data, extract useful information from the image and preserve significant structural properties of an input image. Further, these edges can be used for object and facial expression detection. In this paper, we will propose new intuitionistic fuzzy divergence and entropy measures with its proof of validity for intuitionistic fuzzy sets. A new and significant technique has been developed for edge detection. To check the robustness of the proposed method, obtained results are compared with Canny, Sobel and Chaira methods. Finally, mean square error (MSE) and peak signal-to-noise ratio (PSNR) have been calculated and PSNR values of proposed method are always equal or greater than the PSNR values of existing methods. The detected edges of the various sample images are found to be true, smooth and sharpen.
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paper_title: Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making

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We introduce a wide range of induced and linguistic generalized aggregation operators. First, we present the induced linguistic generalized ordered weighted averaging (ILGOWA) operator. It is a generalization of the OWA operator that uses linguistic variables, order inducing variables and generalized means in order to provide a more general formulation. One of its main results is that it includes a wide range of linguistic aggregation operators such as the induced linguistic OWA (ILOWA), the induced linguistic OWG (ILOWG) and the linguistic generalized OWA (LGOWA) operator. We further generalize the ILGOWA operator by using quasi-arithmetic means obtaining the induced linguistic quasi-arithmetic OWA (Quasi-ILOWA) operator and by using hybrid averages forming the induced linguistic generalized hybrid average (ILGHA) operator. We also present a further extension with Choquet integrals. We call it the induced linguistic generalized Choquet integral aggregation (ILGCIA). We end the paper with an application of the new approach in a linguistic group decision making problem.
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paper_title: Interval-Valued Intuitionistic Uncertain Linguistic Information-Based TOPSIS Method for Multi-criteria Group Decision-Making Problems

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An interval-valued intuitionistic uncertain linguistic set (IVIULS) combines the ambiguity, fuzziness as well as indeterminacy in real-life predicaments due to intricacy of subjective nature of human thoughts and easily express fuzzy information. Technique for order preference by similarity to an ideal solution (TOPSIS) is one of the eminent traditional distance measure-based approach for multi-criteria group decision-making (MCGDM) problems and having widespread applications. This study aims to develop TOPSIS method for MCGDM problems under IVIUL environment. Firstly, some basic operational laws and aggregation operators of IVIULS are discussed. A novel distance measure of IVIULEs is also investigated. An illustrative example of evaluation problem is also taken to clarify developed methodology and to reveal its efficiency with comparative analysis of proposed method.
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paper_title: Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making

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With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods.
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paper_title: A military airport location selection by AHP integrated PROMETHEE and VIKOR methods

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Abstract This paper presents a location selection problem for a military airport using multiple criteria decision making methods. A real-world decision problem is presented and the decision criteria to evaluate alternative locations are specified. The objective is to identify the best location among candidate locations. Nine main criteria and thirty-three sub-criteria are identified by taking into account not only requirements for a military airport such as climate, geography, infrastructure, security, and transportation but also its environmental and social effects. The criteria weights are determined using AHP. Ranking and selection processes of four alternatives are carried out using PROMETHEE and VIKOR methods. Furthermore, the results of PROMETHEE and VIKOR methods are compared with the results of COPRAS, MAIRCA and MABAC methods. All methods suggest the same alternative as the best and produce the same results on the rankings of the location alternatives. One-way sensitivity analysis is carried out on the main criteria weights for all methods. Statistically significant correlations are observed between the rankings of the methods. Therefore, it is concluded that PROMETHEE, VIKOR, COPRAS, MAIRCA and MABAC methods can be successfully used for location selection problems and in general, for other types of multi-criteria decision problems with finite number of alternatives.
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paper_title: Some geometric aggregation operators based on intuitionistic fuzzy sets

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The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.
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paper_title: An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect

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This paper presents a new interpretation of intuitionistic fuzzy sets in the framework of the Dempster-Shafer theory of evidence (DST). This interpretation makes it possible to represent all mathematical operations on intuitionistic fuzzy values as the operations on belief intervals. Such approach allows us to use directly the Dempster's rule of combination to aggregate local criteria presented by intuitionistic fuzzy values in the decision making problem. The usefulness of the developed method is illustrated with the known example of multiple criteria decision making problem. The proposed approach and a new method for interval comparison based on DST, allow us to solve multiple criteria decision making problem without intermediate defuzzification when not only criteria, but their weights are intuitionistic fuzzy values.
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paper_title: Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making

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Abstract With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of intuitionistic uncertain linguistic variables, some new intuitionistic uncertain linguistic Heronian mean operators, such as intuitionistic uncertain linguistic arithmetic Heronian mean (IULAHM) operator, intuitionistic uncertain linguistic weighted arithmetic Heronian mean (IULWAHM) operator, intuitionistic uncertain linguistic geometric Heronian mean (IULGHM) operator, and intuitionistic uncertain linguistic weighted geometric Heronian mean (IULWGHM) operator, are proposed. Furthermore, we have studied some desired properties of these operators and discussed some special cases with respect to the different parameter values in these operators. Moreover, with respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic uncertain linguistic variables, some approaches based on the developed operators are proposed. Finally, an illustrative example has been given to show the steps of the developed methods and to discuss the influences of different parameters on the decision-making results.
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paper_title: Model for evaluating the design patterns of the Micro-Air vehicle under interval-valued intuitionistic uncertain linguistic environment

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The problem for evaluating the design patterns of the Micro-Air vehicle is the multiple attribute decision making problems. In this paper, we introduce the concept of interval-valued intuitionistic uncertain linguistic sets and propose the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (I-IVIULOWA) operator on the basis of the interval-valued intuitionistic uncertain linguistic ordered weighted average (IVIULOWA) operator and IOWA operator. We also study some desirable properties of the proposed operator, such as commutativity, idempotency and monotonicity. Then, we utilize the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (IIVIULOWA) operator to solve the multiple attribute decision making problems with interval-valued intuitionistic uncertain linguistic information. Finally, an illustrative example for evaluating the design patterns of the Micro-Air vehicle is given.
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paper_title: Intuitionistic fuzzy sets

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A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
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paper_title: More on intuitionistic fuzzy sets

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Abstract New results on intuitionistic fuzzy sets are introduced. Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied.
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paper_title: Group decision making approach based on interval-valued intuitionistic linguistic geometric aggregation operators

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In this paper, a new concept of interval-valued intuitionistic linguistic number IVILN, which is characterised by a linguistic term, an interval-valued membership degree and an interval-valued non-membership degree, is first introduced. Then, score function, accuracy function and some multiplicative operational laws of IVILNs are defined. Based on these two functions, a simple approach for the comparison between two IVILNs is presented. Based on these operational laws, some new geometric aggregation operators, such as the interval-valued intuitionistic linguistic weighted geometric IVILWG operator, interval-valued intuitionistic linguistic ordered weighted geometric IVILOWG operator and interval-valued intuitionistic linguistic hybrid geometric IVILHG operator, are proposed, and some desirable properties of these operators are established. Furthermore, by using the IVILWG operator and the IVILHG operator, a group decision making approach, in which the criterion values are IVILNs and the criterion weight information is known completely, is developed. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.
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paper_title: Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making

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Abstract In this study a generated admissible order between interval-valued intuitionistic uncertain linguistic numbers using two continuous functions is introduced. Then, two interval-valued intuitionistic uncertain linguistic operators called the interval-valued intuitionistic uncertain linguistic Choquet averaging (IVIULCA) operator and the interval-valued intuitionistic uncertain linguistic Choquet geometric mean (IVIULCGM) operator are defined, which consider the interactive characteristics among elements in a set. In order to overall reflect the correlations between them, we further define the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet averaging (GS-IVIULCA) operator and the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet geometric mean (GS-IVIULCGM) operator. Moreover, if the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on expert set and attribute set are established, respectively. Finally, a method to multi-attribute group decision making under interval-valued intuitionistic uncertain linguistic environment is developed, and an example is provided to show the specific application of the developed procedure.
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paper_title: The symmetrical interval intuitionistic uncertain linguistic operators and their application to decision making

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We point out the issues of the operational laws on IIULSs in the reference.We define some new operational laws that eliminate the existing issues.The expected and accuracy functions are defined to rank IIULSs.Two operators on IIULSs are defined, and optimal models are established.An approach is developed, and the associated example is offered. Interval intuitionistic uncertain linguistic sets are an important generalization of fuzzy sets, which well cope with the experts' qualitative preferences as well as reflect the interval membership and non-membership degrees of the uncertain linguistic term. This paper first points out the issues of the operational laws on interval intuitionistic uncertain linguistic numbers in the literature, and then defines some alternative ones. To consider the relationship between interval intuitionistic uncertain linguistic sets, the expectation and accuracy functions are defined. To study the application of interval intuitionistic uncertain linguistic sets, two symmetrical interval intuitionistic uncertain linguistic hybrid aggregation operators are defined. Meanwhile, models for the optimal weight vectors are established, by which the optimal weighting vector can be obtained. As a series of development, an approach to multi-attribute decision making under interval intuitionistic uncertain linguistic environment is developed, and the associated example is provided to demonstrate the effectivity and practicality of the procedure.
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paper_title: Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making

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The intuitionistic uncertain fuzzy linguistic variable can easily expressthe fuzzy information, and the power average (PA) operator is a usefultool which provides more versatility in the information aggregation procedure.At the same time, Einstein operations are a kind of various t-normsand t-conorms families which can be used to perform the corresponding intersectionsand unions of intuitionistic fuzzy sets (IFSs). In this paper, wewill combine the PA operator and Einstein operations to intuitionistic uncertainlinguistic environment, and propose some new PA operators. Firstly,the definition and some basic operations of intuitionistic uncertain linguisticnumber (IULN), power aggregation (PA) operator and Einstein operationsare introduced. Then, we propose intuitionistic uncertain linguistic fuzzypowered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguisticfuzzy powered Einstein weighted (IULFPEWA) operator, intuitionisticuncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionisticuncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG)operator, and discuss some properties of them in detail. Furthermore, we developthe decision making methods for multi-attribute group decision making(MAGDM) problems with intuitionistic uncertain linguistic information andgive the detail decision steps. At last, an illustrate example is given to showthe process of decision making and the effectiveness of the proposed method.
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paper_title: Intuitionistic Fuzzy Linguistic Induced Ordered Weighted Averaging Operator for Group Decision Making

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With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of intuitionistic fuzzy linguistic variables, a decision analysis approach is proposed. In this paper, we develop an intuitionistic fuzzy linguistic induce OWA (IFLIOWA) operator and analyze the properties of it by utilizing some operational laws of intuitionistic fuzzy linguistic variables. A new method based on the IFLIOWA operator for multiple attribute group decision making (MAGDM) is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.
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paper_title: Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making

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With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic linguistic numbers, the group decision making methods based on some generalized dependent aggregation operators are developed. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic generalized dependent ordered weighted average (ILGDOWA) operator and an intuitionistic linguistic generalized dependent hybrid weighted aggregation (ILGDHWA) operator are developed. Furthermore, some desirable properties of the ILGDOWA operator, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILGDOWA and ILGDHWA operators, the approach to multiple attribute group decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: INTUITIONISTIC UNCERTAIN LINGUISTIC WEIGHTED BONFERRONI OWA OPERATOR AND ITS APPLICATION TO MULTIPLE ATTRIBUTE DECISION MAKING

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With respect to multiple attribute decision making (MADM) problems, in which attribute values take the form of intuitionistic uncertain linguistic information, a new decision-making method based on the intuitionistic uncertain linguistic weighted Bonferroni OWA operator is developed. First, the score function, accuracy function, and comparative method of the intuitionistic uncertain linguistic numbers are introduced. Then, an intuitionistic uncertain linguistic Bonferroni OWA (IULBOWA) operator and an intuitionistic uncertain linguistic weighted Bonferroni OWA (IULWBOWA) operator are developed. Furthermore, some properties of the IULBOWA and IULWBOWA operators, such as commutativity, idempotency, monotonicity, and boundedness, are discussed. At the same time, some special cases of these operators are analyzed. Based on the IULWBOWA operator, the multiple attribute decision-making method with intuitionistic uncertain linguistic information is proposed. Finally, an illustrative example is given to illustrat...
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paper_title: δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

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Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197–206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM).
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paper_title: Improved Accuracy Function for Interval-Valued Intuitionistic Fuzzy Sets and Its Application to Multi–Attributes Group Decision Making

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ABSTRACTAccuracy functions proposed by various researchers fail to compare some interval-valued intuitionistic fuzzy sets (IVIFSs) correctly. In the present research paper, we propose an improved accuracy function to compare all comparable IVIFSs correctly. The use of proposed accuracy function is also proposed in a method for multi attribute group decision making (MAGDM) method with partially known attributes’ weight. Finally, the proposed MAGDM method is implemented on a real case study of evaluation teachers’ performance. Sensitivity analysis of this method is also done to show the effectiveness of the proposed accuracy function in MAGDM.
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paper_title: Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators

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With respect to multiple attribute group decision making (MADM) problems in which attribute values take the form of intuitionistic linguistic numbers, some new group decision making methods are developed. Firstly, some operational laws, expected value, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic power generalized weighted average (ILPGWA) operator and an intuitionistic linguistic power generalized ordered weighted average (ILPGOWA) operator are developed. Furthermore, some desirable properties of the ILPGWA and ILPGOWA operators, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILPGWA and ILPGOWA operators, two approaches to multiple attribute group decision making with intuitionistic linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: Induced ordered weighted averaging operators

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We briefly describe the Ordered Weighted Averaging (OWA) operator and discuss a methodology for learning the associated weighting vector from observational data. We then introduce a more general type of OWA operator called the Induced Ordered Weighted Averaging (IOWA) Operator. These operators take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are then aggregated. A number of different aggregation situations have been shown to be representable in this framework. We then show how this tool can be used to represent different types of aggregation models.
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paper_title: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment

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In this paper, two uncertain linguistic aggregation operators called uncertain linguistic ordered weighted averaging (ULOWA) operator and uncertain linguistic hybrid aggregation (ULHA) operator are proposed. An approach to multiple attribute group decision making with uncertain linguistic information is developed based on the ULOWA and the ULHA operators. Finally, a practical application of the developed approach to the problem of evaluating university faculty for tenure and promotion is given.
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paper_title: Autocratic multiattribute group decision making for hotel location selection based on interval-valued intuitionistic fuzzy sets

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Abstract In this paper, we propose a new autocratic multiattribute group decision making (AMAGDM) method for hotel location selection based on interval-valued intuitionistic fuzzy sets (IVIFSs), where the evaluating values of the attributes for alternatives and the weights of the attributes given by decision makers are represented by interval-valued intuitionistic fuzzy values (IVIFVs). The proposed method calculates the changing of the weights of the decision makers until the group consensus degree (GCD) of the decision makers is larger than or equal to a predefined threshold value. We also apply the proposed AMAGDM method to deal with the hotel location selection problem. The main contribution of this paper is that we propose a new AMAGDM method which is simpler than Wibowo's method (2013), where the drawback of Wibowo's method is that it is too complicated due to the fact that it adopts the concept of ideal solutions for determining the overall performance of each hotel location alternative with respect to all the selection criteria. The proposed AMAGDM method provides us with a very useful way for AMAGDM in interval-valued intuitionistic fuzzy environments.
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paper_title: A new multiattribute decision making method based on multiplication operations of interval-valued intuitionistic fuzzy values and linear programming methodology

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Abstract In this paper, we propose a new method for multiattribute decision making (MADM) using multiplication operations of interval-valued intuitionistic fuzzy values (IVIFVs) and the linear programming (LP) methodology. It can overcome the shortcomings of Chen and Huang's MADM method (2017), where Chen and Huang's MADM method has two shortcomings, i.e., (1) it gets an infinite number of solutions of the optimal weights of attributes when the summation values of some columns in the transformed decision matrix (TDM) are the same, resulting in the case that it obtains different preference orders (POs) of the alternatives, and (2) the PO of alternatives cannot be distinguished in some situations.
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paper_title: Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making

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With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of intuitionistic uncertain linguistic variables, new group decision making methods have been developed. First, operational laws, expected value definitions, score functions and accuracy functions of intuitionistic uncertain linguistic variables are introduced. Then, an intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator and an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator are developed. Furthermore, some desirable properties of these operators, such as commutativity, idempotency, monotonicity and boundedness, have been studied, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, was developed. Based on these operators, two methods for multiple attribute group decision making problems with intuitionistic uncertain linguistic information have been proposed. Finally, an illustrative example is given to verify the developed approaches and demonstrate their practicality and effectiveness.
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paper_title: An extended TOPSIS method for the multiple attribute group decision making problems based on intuitionistic linguistic numbers

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With respect to the multiple attribute group decision making problems in which the attribute weights are unknown and the attribute values take the form of the intuitionistic linguistic numbers, an expanded technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Firstly, the definition of intuitionistic linguistic number and the operational laws are given and distance between intuitionistic linguistic numbers is defined. Then, the attribute weights are determined based on the ‘maximizing deviation method’ and an extended TOPSIS method is developed to rank the alternatives. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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paper_title: On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

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In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.
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paper_title: On generalized induced linguistic aggregation operators

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In this paper, we define various generalized induced linguistic aggregation operators, including generalized induced linguistic ordered weighted averaging (GILOWA) operator, generalized induced linguistic ordered weighted geometric (GILOWG) operator, generalized induced uncertain linguistic ordered weighted averaging (GIULOWA) operator, generalized induced uncertain linguistic ordered weighted geometric (GIULOWG) operator, etc. Each object processed by these operators consists of three components, where the first component represents the importance degree or character of the second component, and the second component is used to induce an ordering, through the first component, over the third components which are linguistic variables (or uncertain linguistic variables) and then aggregated. It is shown that the induced linguistic ordered weighted averaging (ILOWA) operator and linguistic ordered weighted averaging (LOWA) operator are the special cases of the GILOWA operator, induced linguistic ordered weighted geometric (ILOWG) operator and linguistic ordered weighted geometric (LOWG) operator are the special cases of the GILOWG operator, the induced uncertain linguistic ordered weighted averaging (IULOWA) operator and uncertain linguistic ordered weighted averaging (ULOWA) operator are the special cases of the GIULOWA operator, and that the induced uncertain linguistic ordered weighted geometric (IULOWG) operator and uncertain LOWG operator are the special cases of the GILOWG operator.
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paper_title: An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation

paper_content:

Abstract In the process of multi-criteria decision making (MCDM), decision makers or experts usually exploit quantitative or qualitative methods to evaluate the comprehensive performance of all alternatives on each criterion. How the decision-makers or the experts make the evaluations relies on their professional knowledge and the actual performances on the criteria characters of the alternatives. However, because of both the objective complexity of decision making problem and the uncertainty of human subjective judgments, it is sometimes too hard to get the accurate evaluation information. Intuitionistic fuzzy set (IFS) is a useful tool to deal with uncertainty and fuzziness of complex problems. In this paper, we propose a new distance measure between IFSs and prove some of its useful properties. The experimental results show that the proposed distance measure between IFSs can overcome the drawbacks of some existing distance and similarity measures. Then based on the proposed distance measure, an extended intuitionistic fuzzy TOPSIS approach is developed to handle the MCDM problems. Finally, a practical application which is about credit risk evaluation of potential strategic partners is provided to demonstrate the extended intuitionistic fuzzy TOPSIS approach, and then it is compared with other current methods to further explain its effectiveness.
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paper_title: Group decision making approach based on interval-valued intuitionistic linguistic geometric aggregation operators

paper_content:

In this paper, a new concept of interval-valued intuitionistic linguistic number IVILN, which is characterised by a linguistic term, an interval-valued membership degree and an interval-valued non-membership degree, is first introduced. Then, score function, accuracy function and some multiplicative operational laws of IVILNs are defined. Based on these two functions, a simple approach for the comparison between two IVILNs is presented. Based on these operational laws, some new geometric aggregation operators, such as the interval-valued intuitionistic linguistic weighted geometric IVILWG operator, interval-valued intuitionistic linguistic ordered weighted geometric IVILOWG operator and interval-valued intuitionistic linguistic hybrid geometric IVILHG operator, are proposed, and some desirable properties of these operators are established. Furthermore, by using the IVILWG operator and the IVILHG operator, a group decision making approach, in which the criterion values are IVILNs and the criterion weight information is known completely, is developed. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.
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paper_title: The symmetrical interval intuitionistic uncertain linguistic operators and their application to decision making

paper_content:

We point out the issues of the operational laws on IIULSs in the reference.We define some new operational laws that eliminate the existing issues.The expected and accuracy functions are defined to rank IIULSs.Two operators on IIULSs are defined, and optimal models are established.An approach is developed, and the associated example is offered. Interval intuitionistic uncertain linguistic sets are an important generalization of fuzzy sets, which well cope with the experts' qualitative preferences as well as reflect the interval membership and non-membership degrees of the uncertain linguistic term. This paper first points out the issues of the operational laws on interval intuitionistic uncertain linguistic numbers in the literature, and then defines some alternative ones. To consider the relationship between interval intuitionistic uncertain linguistic sets, the expectation and accuracy functions are defined. To study the application of interval intuitionistic uncertain linguistic sets, two symmetrical interval intuitionistic uncertain linguistic hybrid aggregation operators are defined. Meanwhile, models for the optimal weight vectors are established, by which the optimal weighting vector can be obtained. As a series of development, an approach to multi-attribute decision making under interval intuitionistic uncertain linguistic environment is developed, and the associated example is provided to demonstrate the effectivity and practicality of the procedure.
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paper_title: Atanassov's intuitionistic linguistic ordered weighted averaging distance operator and its application to decision making

paper_content:

In this paper, we introduce the Atanassov's intuitionistic linguistic ordered weighted averaging distance AILOWAD operator. It is a new aggregation operator that unifies distance measures and Atanassov's intuitionistic linguistic variables in the ordered weighted averaging OWA operator. The main advantage of this aggregation operator is that it is able to use the attitudinal character of the decision maker in the aggregation of the distance measures. Moreover, it is able to deal with uncertain situations where the information can assessed with Atanassov's intuitionistic linguistic numbers. We study some of main properties and different particular cases of the AILOWAD operator. We further generalize this approach by using quasi-arithmetic means obtaining the quasi-arithmetic AILOWAD Quasi-AILOWAD operator. We also develop an application of the new approach to a multi-person decision making problem regarding the selection of strategies. Thus, we obtain the multi-person AILOWAD MP-AILOWAD operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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paper_title: An Intuitionistic 2-Tuple Linguistic Information Model and Aggregation Operators

paper_content:

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Fuzzy sets was presented to manage situations in which experts have some membership value to assess an alternative. The fuzzy linguistic approach has been applied successfully to many problems. The linguistic information expressed by means of 2-tuples, which were composed by a linguistic term and a numeric value assessed in [ - 0.5, 0.5. Linguistic values was used to assess an alternative and variable in qualitative settings. Intuitionistic fuzzy sets were presented to manage situations in which experts have some membership and nonmembership value to assess an alternative. In this paper, the concept of an I2LI model is developed to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible and impossible linguistic variable and their translation parameter. A method to solve the group decision making problem based on intuitionistic 2-tuple linguistic information I2LI by the group of experts is formulated. Some operational laws on I2LI are introduced. Based on these laws, new aggregation operators are introduced to aggregate the collective opinion of decision makers. An illustrative example is given to show the practicality and feasibility of our proposed aggregation operators and group decision making method.
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paper_title: Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making

paper_content:

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of intuitionistic uncertain linguistic variables, new group decision making methods have been developed. First, operational laws, expected value definitions, score functions and accuracy functions of intuitionistic uncertain linguistic variables are introduced. Then, an intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator and an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator are developed. Furthermore, some desirable properties of these operators, such as commutativity, idempotency, monotonicity and boundedness, have been studied, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, was developed. Based on these operators, two methods for multiple attribute group decision making problems with intuitionistic uncertain linguistic information have been proposed. Finally, an illustrative example is given to verify the developed approaches and demonstrate their practicality and effectiveness.
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paper_title: Interval-Valued Intuitionistic Uncertain Linguistic Information-Based TOPSIS Method for Multi-criteria Group Decision-Making Problems

paper_content:

An interval-valued intuitionistic uncertain linguistic set (IVIULS) combines the ambiguity, fuzziness as well as indeterminacy in real-life predicaments due to intricacy of subjective nature of human thoughts and easily express fuzzy information. Technique for order preference by similarity to an ideal solution (TOPSIS) is one of the eminent traditional distance measure-based approach for multi-criteria group decision-making (MCGDM) problems and having widespread applications. This study aims to develop TOPSIS method for MCGDM problems under IVIUL environment. Firstly, some basic operational laws and aggregation operators of IVIULS are discussed. A novel distance measure of IVIULEs is also investigated. An illustrative example of evaluation problem is also taken to clarify developed methodology and to reveal its efficiency with comparative analysis of proposed method.
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paper_title: An extended TOPSIS method for the multiple attribute group decision making problems based on intuitionistic linguistic numbers

paper_content:

With respect to the multiple attribute group decision making problems in which the attribute weights are unknown and the attribute values take the form of the intuitionistic linguistic numbers, an expanded technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Firstly, the definition of intuitionistic linguistic number and the operational laws are given and distance between intuitionistic linguistic numbers is defined. Then, the attribute weights are determined based on the ‘maximizing deviation method’ and an extended TOPSIS method is developed to rank the alternatives. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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paper_title: An extended TODIM method for multiple attribute group decision making based on intuitionistic uncertain linguistic variables

paper_content:

The intuitionistic uncertain linguistic variables are the good tools to express the fuzzy information, and the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method can consider the bounded rationality of decision makers based on the prospect theory. However, the classical TODIM method can only process the multiple attribute decision making (MADM) problems where the attribute values take the form of crisp numbers. In this paper, we will extend the TODIM method to the multiple attribute group decision making (MAGDM) with intuitionistic uncertain linguistic information. Firstly, the definition, characteristics, expectation, comparison method and distance of intuitionistic uncertain linguistic variables are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MAGDM problems with intuitionistic uncertain linguistic variables, and its significant characteristic is that it can fully consider the decision makers' bounded rationality which is a real action in decision making. Finally, an illustrative example is proposed to verify the developed approach.
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paper_title: Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making

paper_content:

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic linguistic numbers, the group decision making methods based on some generalized dependent aggregation operators are developed. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic generalized dependent ordered weighted average (ILGDOWA) operator and an intuitionistic linguistic generalized dependent hybrid weighted aggregation (ILGDHWA) operator are developed. Furthermore, some desirable properties of the ILGDOWA operator, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILGDOWA and ILGDHWA operators, the approach to multiple attribute group decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators

paper_content:

With respect to multiple attribute group decision making (MADM) problems in which attribute values take the form of intuitionistic linguistic numbers, some new group decision making methods are developed. Firstly, some operational laws, expected value, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic power generalized weighted average (ILPGWA) operator and an intuitionistic linguistic power generalized ordered weighted average (ILPGOWA) operator are developed. Furthermore, some desirable properties of the ILPGWA and ILPGOWA operators, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILPGWA and ILPGOWA operators, two approaches to multiple attribute group decision making with intuitionistic linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making

paper_content:

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods.
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paper_title: Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making

paper_content:

Abstract With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of intuitionistic uncertain linguistic variables, some new intuitionistic uncertain linguistic Heronian mean operators, such as intuitionistic uncertain linguistic arithmetic Heronian mean (IULAHM) operator, intuitionistic uncertain linguistic weighted arithmetic Heronian mean (IULWAHM) operator, intuitionistic uncertain linguistic geometric Heronian mean (IULGHM) operator, and intuitionistic uncertain linguistic weighted geometric Heronian mean (IULWGHM) operator, are proposed. Furthermore, we have studied some desired properties of these operators and discussed some special cases with respect to the different parameter values in these operators. Moreover, with respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic uncertain linguistic variables, some approaches based on the developed operators are proposed. Finally, an illustrative example has been given to show the steps of the developed methods and to discuss the influences of different parameters on the decision-making results.
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paper_title: Power-Geometric Operators and Their Use in Group Decision Making

paper_content:

The power-average (PA) operator and the power-ordered-weighted-average (POWA) operator are the two nonlinear weighted-average aggregation tools whose weighting vectors depend on the input arguments. In this paper, we develop a power-geometric (PG) operator and its weighted form, which are on the basis of the PA operator and the geometric mean, and develop a power-ordered-geometric (POG) operator and a power-ordered-weighted-geometric (POWG) operator, which are on the basis of the POWA operator and the geometric mean, and study some of their properties. We also discuss the relationship between the PA and PG operators and the relationship between the POWA and POWG operators. Then, we extend the PG and POWG operators to uncertain environments, i.e., develop an uncertain PG (UPG) operator and its weighted form, and an uncertain power-ordered-weighted-geometric (UPOWG) operator to aggregate the input arguments taking the form of interval of numerical values. Furthermore, we utilize the weighted PG and POWG operators, respectively, to develop an approach to group decision making based on multiplicative preference relations and utilize the weighted UPG and UPOWG operators, respectively, to develop an approach to group decision making based on uncertain multiplicative preference relations. Finally, we apply both the developed approaches to broadband Internet-service selection.
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paper_title: INTUITIONISTIC UNCERTAIN LINGUISTIC WEIGHTED BONFERRONI OWA OPERATOR AND ITS APPLICATION TO MULTIPLE ATTRIBUTE DECISION MAKING

paper_content:

With respect to multiple attribute decision making (MADM) problems, in which attribute values take the form of intuitionistic uncertain linguistic information, a new decision-making method based on the intuitionistic uncertain linguistic weighted Bonferroni OWA operator is developed. First, the score function, accuracy function, and comparative method of the intuitionistic uncertain linguistic numbers are introduced. Then, an intuitionistic uncertain linguistic Bonferroni OWA (IULBOWA) operator and an intuitionistic uncertain linguistic weighted Bonferroni OWA (IULWBOWA) operator are developed. Furthermore, some properties of the IULBOWA and IULWBOWA operators, such as commutativity, idempotency, monotonicity, and boundedness, are discussed. At the same time, some special cases of these operators are analyzed. Based on the IULWBOWA operator, the multiple attribute decision-making method with intuitionistic uncertain linguistic information is proposed. Finally, an illustrative example is given to illustrat...
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paper_title: The power average operator

paper_content:

We introduce the power average to provide an aggregation operator which allows argument values to support each other in the aggregation process. The properties of this operator are described. We discuss the idea of a power median. We introduce some possible formulations for the support function used in the power average. We extend the supported aggregation facility of empowerment to a wider class of mean operators, such as the OWA (ordered weighted averaging) operator and the generalized mean operator.
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paper_title: A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety

paper_content:

Coal mine safety has been a pressing issue for many years, and it is a constant and non-negligible problem that must be addressed during any coal mining process. This paper focuses on developing an innovative multi-criteria decision-making (MCDM) method to address coal mine safety evaluation problems. Because lots of uncertain and fuzzy information exists in the process of evaluating coal mine safety, linguistic intuitionistic fuzzy numbers (LIFNs) are introduced to depict the evaluation information necessary to the process. Furthermore, the handling of qualitative information requires the effective support of quantitative tools, and the linguistic scale function (LSF) is therefore employed to deal with linguistic intuitionistic information. First, the distance, a valid ranking method, and Frank operations are proposed for LIFNs. Subsequently, the linguistic intuitionistic fuzzy Frank improved weighted Heronian mean (LIFFIWHM) operator is developed. Then, a linguistic intuitionistic MCDM method for coal mine safety evaluation is constructed based on the developed operator. Finally, an illustrative example is provided to demonstrate the proposed method, and its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.
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paper_title: Induced generalized intuitionistic fuzzy operators

paper_content:

We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster-Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster-Shafer operators. Then we investigate their various properties and some of their special cases. Additionally, we apply the developed operators to financial decision making under intuitionistic fuzzy environments. Some extensions in interval-valued intuitionistic fuzzy situations are also pointed out.
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paper_title: Intuitionistic Fuzzy Aggregation Operators

paper_content:

An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
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paper_title: Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making

paper_content:

We introduce a wide range of induced and linguistic generalized aggregation operators. First, we present the induced linguistic generalized ordered weighted averaging (ILGOWA) operator. It is a generalization of the OWA operator that uses linguistic variables, order inducing variables and generalized means in order to provide a more general formulation. One of its main results is that it includes a wide range of linguistic aggregation operators such as the induced linguistic OWA (ILOWA), the induced linguistic OWG (ILOWG) and the linguistic generalized OWA (LGOWA) operator. We further generalize the ILGOWA operator by using quasi-arithmetic means obtaining the induced linguistic quasi-arithmetic OWA (Quasi-ILOWA) operator and by using hybrid averages forming the induced linguistic generalized hybrid average (ILGHA) operator. We also present a further extension with Choquet integrals. We call it the induced linguistic generalized Choquet integral aggregation (ILGCIA). We end the paper with an application of the new approach in a linguistic group decision making problem.
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paper_title: Intuitionistic Fuzzy Linguistic Induced Ordered Weighted Averaging Operator for Group Decision Making

paper_content:

With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of intuitionistic fuzzy linguistic variables, a decision analysis approach is proposed. In this paper, we develop an intuitionistic fuzzy linguistic induce OWA (IFLIOWA) operator and analyze the properties of it by utilizing some operational laws of intuitionistic fuzzy linguistic variables. A new method based on the IFLIOWA operator for multiple attribute group decision making (MAGDM) is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.
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paper_title: On generalized induced linguistic aggregation operators

paper_content:

In this paper, we define various generalized induced linguistic aggregation operators, including generalized induced linguistic ordered weighted averaging (GILOWA) operator, generalized induced linguistic ordered weighted geometric (GILOWG) operator, generalized induced uncertain linguistic ordered weighted averaging (GIULOWA) operator, generalized induced uncertain linguistic ordered weighted geometric (GIULOWG) operator, etc. Each object processed by these operators consists of three components, where the first component represents the importance degree or character of the second component, and the second component is used to induce an ordering, through the first component, over the third components which are linguistic variables (or uncertain linguistic variables) and then aggregated. It is shown that the induced linguistic ordered weighted averaging (ILOWA) operator and linguistic ordered weighted averaging (LOWA) operator are the special cases of the GILOWA operator, induced linguistic ordered weighted geometric (ILOWG) operator and linguistic ordered weighted geometric (LOWG) operator are the special cases of the GILOWG operator, the induced uncertain linguistic ordered weighted averaging (IULOWA) operator and uncertain linguistic ordered weighted averaging (ULOWA) operator are the special cases of the GIULOWA operator, and that the induced uncertain linguistic ordered weighted geometric (IULOWG) operator and uncertain LOWG operator are the special cases of the GILOWG operator.
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paper_title: Analysis of socioeconomic development by intuitionistic linguistic fuzzy numbers

paper_content:

Abstract In this paper by using fuzzy intuitionistic linguistic fuzzy operators has been analyzed the influence of external factors to economic state, social consequences and government responses. The analysis is investigated on the basis of Azerbaijan and international information in 2010-2015.
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paper_title: Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators

paper_content:

For multi-criteria group decision making problems with intuitionistic linguistic information, we define a new score function and a new accuracy function of intuitionistic linguistic numbers, and propose a simple approach for the comparison between two intuitionistic linguistic numbers. Based on the intuitionistic linguistic weighted arithmetic averaging ILWAA operator, we define two new intuitionistic linguistic aggregation operators, such as the intuitionistic linguistic ordered weighted averaging ILOWA operator and the intuitionistic linguistic hybrid aggregation ILHA operator, and establish various properties of these operators. The ILOWA operator weights the ordered positions of the intuitionistic linguistic numbers instead of weighting the arguments themselves. The ILHA operator generalizes both the ILWAA operator and the ILOWA operator at the same time, and reflects the importance degrees of both the given intuitionistic linguistic numbers and the ordered positions of these arguments. Furthermore, based on the ILHA operator and the ILWAA operator, we develop a multi-criteria group decision making approach, in which the criteria values are intuitionistic linguistic numbers and the criteria weight information is known completely. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.
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paper_title: Model for evaluating the design patterns of the Micro-Air vehicle under interval-valued intuitionistic uncertain linguistic environment

paper_content:

The problem for evaluating the design patterns of the Micro-Air vehicle is the multiple attribute decision making problems. In this paper, we introduce the concept of interval-valued intuitionistic uncertain linguistic sets and propose the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (I-IVIULOWA) operator on the basis of the interval-valued intuitionistic uncertain linguistic ordered weighted average (IVIULOWA) operator and IOWA operator. We also study some desirable properties of the proposed operator, such as commutativity, idempotency and monotonicity. Then, we utilize the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (IIVIULOWA) operator to solve the multiple attribute decision making problems with interval-valued intuitionistic uncertain linguistic information. Finally, an illustrative example for evaluating the design patterns of the Micro-Air vehicle is given.
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paper_title: An Intuitionistic 2-Tuple Linguistic Information Model and Aggregation Operators

paper_content:

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Fuzzy sets was presented to manage situations in which experts have some membership value to assess an alternative. The fuzzy linguistic approach has been applied successfully to many problems. The linguistic information expressed by means of 2-tuples, which were composed by a linguistic term and a numeric value assessed in [ - 0.5, 0.5. Linguistic values was used to assess an alternative and variable in qualitative settings. Intuitionistic fuzzy sets were presented to manage situations in which experts have some membership and nonmembership value to assess an alternative. In this paper, the concept of an I2LI model is developed to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible and impossible linguistic variable and their translation parameter. A method to solve the group decision making problem based on intuitionistic 2-tuple linguistic information I2LI by the group of experts is formulated. Some operational laws on I2LI are introduced. Based on these laws, new aggregation operators are introduced to aggregate the collective opinion of decision makers. An illustrative example is given to show the practicality and feasibility of our proposed aggregation operators and group decision making method.
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paper_title: Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators

paper_content:

With respect to multiple attribute group decision making (MADM) problems in which attribute values take the form of intuitionistic linguistic numbers, some new group decision making methods are developed. Firstly, some operational laws, expected value, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic power generalized weighted average (ILPGWA) operator and an intuitionistic linguistic power generalized ordered weighted average (ILPGOWA) operator are developed. Furthermore, some desirable properties of the ILPGWA and ILPGOWA operators, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILPGWA and ILPGOWA operators, two approaches to multiple attribute group decision making with intuitionistic linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
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paper_title: A new extension to PROMETHEE under intuitionistic fuzzy environment for solving supplier selection problem with linguistic preferences

paper_content:

Abstract This paper presents a new two-tier decision making framework with linguistic preferences for scientific decision making. The major reason for adopting linguistic preference is to ease the process of rating of alternatives by allowing decision makers (DMs) to strongly emphasize their opinion on each alternative. In the first tier, aggregation is done using a newly proposed operator called linguistic based aggregation (LBA), which aggregates linguistic terms directly without making any conversion. The main motivation for this proposal is driven by the previous studies on aggregation theory which reveals that conversion leads to loss of information and formation of virtual sets which are no longer sensible and rational for decision making process. Secondly, in the next tier, a new ranking method called IFSP (intuitionistic fuzzy set based PROMETHEE) is proposed which is an extension to PROMETHEE (preference ranking organization method for enrichment evaluation) under intuitionistic fuzzy set (IFS) context. Unlike previous ranking methods, this ranking method follows a new formulation by considering personal choice of the DMs over each alternative. The main motivation for such formulation is derived from the notion of not just obtaining a suitable alternative but also coherently satisfying the DMs’ viewpoint during decision process. Finally, the practicality of the framework is tested by using supplier selection (SS) problem for an automobile factory. The strength and weakness of the proposed LBA-IFSP framework are verified by comparing with other methods under the realm of theoretical and numerical analysis. The results from the analysis infer that proposed LBA-IFSP framework is rationally coherent to DMs’ viewpoint, moderately consistent with other methods and highly stable and robust against rank reversal issue.
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paper_title: Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making

paper_content:

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of intuitionistic uncertain linguistic variables, new group decision making methods have been developed. First, operational laws, expected value definitions, score functions and accuracy functions of intuitionistic uncertain linguistic variables are introduced. Then, an intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator and an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator are developed. Furthermore, some desirable properties of these operators, such as commutativity, idempotency, monotonicity and boundedness, have been studied, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, was developed. Based on these operators, two methods for multiple attribute group decision making problems with intuitionistic uncertain linguistic information have been proposed. Finally, an illustrative example is given to verify the developed approaches and demonstrate their practicality and effectiveness.
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paper_title: An approach to evaluating the knowledge management performance with interval-valued intuitionistic uncertain linguistic information

paper_content:

In this paper, we first introduce some operations on interval-valued intuitionistic uncertain linguistic sets, and further develop the induced interval-valued intuitionistic uncertain linguistic ordered weighted geometric (I-IVIULOWG) operator. We also establish some desirable properties of this operator, such as commutativity, idempotency and monotonicity. Then, we apply the induced interval-valued intuitionistic uncertain linguistic ordered weighted geometric (I-IVIULOWG) operator to deal with the interval-valued intuitionistic uncertain linguistic multiple attribute decision making problems. Finally, an illustrative example for evaluating the knowledge management performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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paper_title: Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making

paper_content:

Intuitionistic fuzzy information aggregation plays an important part in intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we investigate the multiple attribute decision making (MADM) problems with intuitionistic fuzzy numbers. Then, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, and Einstein exponentiation, and further develop some new Einstein hybrid aggregation operators, such as the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator, which extend the hybrid averaging (HA) operator and the hybrid geometric (HG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. Then, we apply the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.
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paper_title: ELECTRE-Based Outranking Method for Multi-criteria Decision Making Using Hesitant Intuitionistic Fuzzy Linguistic Term Sets

paper_content:

An outranking method is developed within the environment of hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), where the membership degree and the non-membership degree of the element are subsets of linguistic term set. The directional Hausdorff distance, which uses HIFLTSs, is proposed, and the dominance relations are subsequently defined using this distance. Moreover, some interesting characteristics of the proposed directional Hausdorff distance are further discussed in detail. In this context, a collective decision matrix is obtained in the form of hesitant intuitionistic fuzzy linguistic elements and analyzes the collective data by using proposed ELECTRE-based outranking method. The linguistic scale functions are employed in this paper to conduct the transformation between qualitative information and quantitative data. Furthermore, based on the proposed method, we also investigate the ranking of the alternatives based on a new proposed definition of HIFLTS. The feasibility and applicability of the proposed method are illustrated with an example, and a comparative analysis is performed with other approaches to validate the effectiveness of the proposed methodology.
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paper_title: Multiple attribute decision-making approach based on dual hesitant fuzzy Frank aggregation operators

paper_content:

Abstract Real-world decision-making problems are often complex and indeterminate. Thus, uncertainty and hesitancy are usually unavoidable issues being experienced by decision makers. Dual hesitant fuzzy sets (DHFSs) which are described in terms of the two functions, namely the membership hesitancy function and the non-membership hesitancy function, have been developed. In light of their properties, they are considered as a powerful vehicle to express uncertain information in the process of multi-attribute decision-making (MADM). In accordance with the practical demand, this study proposes a new MADM approach with dual hesitant fuzzy (DHF) assessments based on Frank aggregation operators. First, original score and accuracy functions of DHFS are developed to construct a new comparison method of DHFSs. The properties of the developed score and accuracy functions are analyzed. Second, we investigate the generalized operations of DHFS based on Frank t-norm and t-conorm. The generalized operations are then used to build the generalized arithmetic and geometric aggregation operators of DHF assessments in the context of fuzzy MADM. The monotonicity of arithmetic and geometric aggregated assessments with respect to a parameter in Frank t-norm and t-conorm and their relationship are also demonstrated. In particular, the monotonicity is employed to associate the parameter with the risk attitude of a decision maker, by which a method is designed to determine the parameter. A procedure of the proposed MADM method is presented. Finally, an investment evaluation problem is discussed by the proposed approach to demonstrate its applicability and validity. A detailed sensitivity analysis and a comparative study are also conducted to highlight the validity and advantages of the approach proposed in this paper. More importantly, we discuss the situations where Frank aggregation operators are replaced by Hamacher aggregation operators at the second step of the proposed approach, through re-considering the investment evaluation problem.
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paper_title: Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator

paper_content:

Normal neutrosophic numbers (NNNs) are an important tool to describe the decision making problems, and they are more appropriate to express the incompleteness, indeterminacy and inconsistency of the evaluation information. In this paper, we firstly introduce the definition, the properties, the score function, the accuracy function, and the operational laws of the NNNs. Then, some operators are proposed, such as the normal neutrosophic power averaging operator, the normal neutrosophic weighted power averaging operator, the normal neutrosophic power geometric operator, the normal neutrosophic weighted power geometric operator, the normal neutrosophic generalized power averaging operator, the normal neutrosophic generalized weighted power averaging (NNGWPA) operator. Furthermore, some properties of them are discussed. Thirdly, we propose a multiple attribute decision making method based on the NNGWPA operator. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.
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paper_title: Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm

paper_content:

Abstract Fuzzy game theory has been applied in many decision-making problems. The matrix game with interval-valued intuitionistic fuzzy numbers (IVIFNs) is investigated based on Archimedean t-conorm and t-norm. The existing matrix games with IVIFNs are all based on Algebraic t-conorm and t-norm, which are special cases of Archimedean t-conorm and t-norm. In this paper, the intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm are employed to aggregate the payoffs of players. To derive the solution of the matrix game with IVIFNs, several mathematical programming models are developed based on Archimedean t-conorm and t-norm. The proposed models can be transformed into a pair of primal–dual linear programming models, based on which, the solution of the matrix game with IVIFNs is obtained. It is proved that the theorems being valid in the exiting matrix game with IVIFNs are still true when the general aggregation operator is used in the proposed matrix game with IVIFNs. The proposed method is an extension of the existing ones and can provide more choices for players. An example is given to illustrate the validity and the applicability of the proposed method.
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paper_title: Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making

paper_content:

Abstract Intuitionistic fuzzy soft set (IFSS) theory is one of the successful extension of the soft set theory to deal the uncertainty by introducing the parametrization factor during the analysis. Under this environment, the present paper develops two new scaled prioritized averaging aggregation operators by considering the interaction between the membership degrees. Further, some shortcomings of the existing operators have been highlighted and overcome by the proposed operators. The principal advantage of the operators is that they consider the priority relationships between the parameters as well as experts. Furthermore, some properties based on these operators are discussed in detail. Then, we utilized these operators to solve decision-making problem and validate it with a numerical example.
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paper_title: Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

paper_content:

The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.
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paper_title: Visualization and quantitative research on intuitionistic fuzzy studies

paper_content:

Since proposed in 1983, the intuitionistic fuzzy set (IFS) theory has grown immensely during the past decades and has wide application in machine learning, pattern recognition, management engineering and decision making. With the rapid development and widespread adoption of IFS, thousands of research results have been appeared, focusing on both theory development and practical applications. Given the large number of research materials exist, this paper intends to make a scientometric review on IFS studies to reveal the most cited papers, influential authors and influential journals in this domain based on the 1318 references retrieved from SCIE and SSCI databases via Web of science. The research results of this paper are based on the objective data analysis and they are less affected by subjective biases, which make them more reliable.
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Title: An overview of intuitionistic linguistic fuzzy information aggregations and applications

Section 1: Introduction
Description 1: Introduce the increasing complexity of decision-making problems, the development of fuzzy set theory, and the need for intuitionistic linguistic fuzzy sets.

Section 2: Basic concepts and operations
Description 2: Discuss the basic concepts and operational rules of different fuzzy sets such as IFS, LTS, ILS, IULS, and IVIULS.

Section 3: Interval-value intuitionistic uncertain linguistic set (IVIULS)
Description 3: Explain the definition and properties of the interval-value intuitionistic uncertain linguistic set.

Section 4: Intuitionistic uncertain 2-tuple linguistic variable (IU2TLV)
Description 4: Define the intuitionistic uncertain 2-tuple linguistic variable and its operational rules.

Section 5: Generalized intuitionistic linguistic fuzzy aggregation operators (GILF AOs)
Description 5: Review the generalized intuitionistic linguistic fuzzy aggregation operators and their applications.

Section 6: Induced IL fuzzy AOs 
Description 6: Discuss the induced intuitionistic linguistic (IL) fuzzy aggregation operators and their characteristics.

Section 7: Applications about the AOs of IULVs
Description 7: Provide an overview of the practical applications of IULVs aggregation operators in different domains, such as project investment and supplier selection.

Section 8: Further research directions
Description 8: Highlight the potential future research directions in the field of intuitionistic linguistic fuzzy information.

Section 9: Conclusions
Description 9: Summarize the key points discussed in the paper and the significance of intuitionistic linguistic fuzzy information in decision-making.