An Overview on Fuzzy Modelling of Complex Linguistic Preferences in Decision Making
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paper_title: An attitude-driven web consensus support system for heterogeneous group decision making

paper_content:

Consensus reaching processes are applied in group decision making problems to reach a mutual agreement among a group of decision makers before making a common decision. Different consensus models have been developed to facilitate consensus reaching processes. However, new trends bring diverse challenges in group decision making, such as the modelling of different types of information and of large groups of decision makers, together with their attitude to achieve agreements. These challenges require the capacity to deal with heterogenous frameworks, and the automation of consensus reaching processes by means of consensus support systems. In this paper, we propose a consensus model in which decision makers can express their opinions by using different types of information, capable of dealing with large groups of decision makers. The model incorporates the management of the group's attitude towards consensus by means of an extension of OWA aggregation operators aimed to optimize the overall consensus process. Eventually, a novel Web-based consensus support system that automates the proposed consensus model is presented.
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paper_title: AN EXTENDED HIERARCHICAL LINGUISTIC MODEL FOR DECISION‐MAKING PROBLEMS

paper_content:

In multi-expert decision making (MEDM) problems the experts provide their preferences about the alternatives according to their knowledge. Because they can have different knowledge, educational backgrounds, or experiences, it seems logical that they might use different evaluation scales to express their opinions. In the present article, we focus on decision problems defined in uncertain contexts where such uncertainty is modeled by means of linguistic information, therefore the decision makers would use different linguistic scales to express their evaluations on the alternatives, i.e., multigranular linguistic scales. Several computational approaches have been presented to manage multigranular linguistic scales in decision problems. Although they provide good results in some cases, still present limitations. A new approach, so-called extended linguistic hierarchies, is presented here for managing multigranular linguistic scales to overcome those limitations, an MEDM case study is given to illustrate the proposed method.
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paper_title: A method based on linguistic aggregation operators for group decision making with linguistic preference relations

paper_content:

In this paper, we define some operational laws of linguistic variables and develop some new aggregation operators such as linguistic geometric averaging (LGA) operator, linguistic weighted geometric averaging (LWGA) operator, linguistic ordered weighted geometric averaging (LOWGA) operator and linguistic hybrid geometric averaging (LHGA) operator, etc., which can be utilized to aggregate preference information taking the form of linguistic variables, and then study some desirable properties of the operators. Based on the LGA and the LHGA operators, we propose a practical method for group decision making with linguistic preference relations. The method is straightforward and has no loss of information. Finally, an illustrative numerical example is also given.
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paper_title: An analysis of symbolic linguistic computing models in decision making

paper_content:

It is common that experts involved in complex real-world decision problems use natural language for expressing their knowledge in uncertain frameworks. The language is inherent vague, hence probabilistic decision models are not very suitable in such cases. Therefore, other tools such as fuzzy logic and fuzzy linguistic approaches have been successfully used to model and manage such vagueness. The use of linguistic information implies to operate with such a type of information, i.e. processes of computing with words (CWW). Different schemes have been proposed to deal with those processes, and diverse symbolic linguistic computing models have been introduced to accomplish the linguistic computations. In this paper, we overview the relationship between decision making and CWW, and focus on symbolic linguistic computing models that have been widely used in linguistic decision making to analyse if all of them can be considered inside of the CWW paradigm.
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paper_title: Environmental impact assessment using the evidential reasoning approach

paper_content:

Environmental impact assessment (EIA) problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments, which inevitably involve various types of uncertainties such as ignorance and fuzziness. So, EIA problems need to be modelled and analysed using methods that can handle uncertainties. The evidential reasoning (ER) approach provides such a modelling framework and analysis method. In this paper the ER approach will be applied to conduct EIA analysis for the first time. The environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive. All assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, is modelled using a unified framework of a belief structure. The original ER approach with a recursive ER algorithm will be introduced and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed such as in optimisation problems. The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy. A numerical example and its modified version are studied to illustrate the detailed implementation process of the ER approach and demonstrate its potential applications in EIA.
---
paper_title: An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges

paper_content:

Many real world problems need to deal with uncertainty, therefore the management of such uncertainty is usually a big challenge. Hence, different proposals to tackle and manage the uncertainty have been developed. Probabilistic models are quite common, but when the uncertainty is not probabilistic in nature other models have arisen such as fuzzy logic and the fuzzy linguistic approach. The use of linguistic information to model and manage uncertainty has given good results and implies the accomplishment of processes of computing with words. A bird's eye view in the recent specialized literature about linguistic decision making, computing with words, linguistic computing models and their applications shows that the 2-tuple linguistic representation model [44] has been widely-used in the topic during the last decade. This use is because of reasons such as, its accuracy, its usefulness for improving linguistic solving processes in different applications, its interpretability, its ease managing of complex frameworks in which linguistic information is included and so forth. Therefore, after a decade of extensive and intensive successful use of this model in computing with words for different fields, it is the right moment to overview the model, its extensions, specific methodologies, applications and discuss challenges in the topic.
---
paper_title: Computing with Words in Decision support Systems: An overview on Models and Applications

paper_content:

Decision making is inherent to mankind, as human beings daily face situations in which they should choose among different alternatives by means of reasoning and mental processes. Many of these decision problems are under uncertain environments with vague and imprecise information. This type of information is usually modelled by linguistic information because of the common use of language by the experts involved in the given decision situations, originating linguistic decision making. The use of linguistic information in decision making demands processes of Computing with Words to solve the related decision problems. Different methodologies and approaches have been proposed to accomplish such processes in an accurate and interpretable way. The good performance of linguistic computing dealing with uncertainty has caused a spread use of it in different types of decision based applications. This paper overviews the more significant and extended linguistic computing models due to its key role in linguistic decision making and a wide range of the most recent applications of linguistic decision support models.
---
paper_title: Hesitant Fuzzy Linguistic Term Sets for Decision Making

paper_content:

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate between several values to assess an indicator, alternative, variable, etc. Hesitant fuzzy sets suit the modeling of quantitative settings; however, similar situations may occur in qualitative settings so that experts think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. Then, a multicriteria linguistic decision-making model is presented in which experts provide their assessments by eliciting linguistic expressions. This decision model manages such linguistic expressions by means of its representation using hesitant fuzzy linguistic term sets.
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paper_title: A new version of 2-tuple fuzzy linguistic representation model for computing with words

paper_content:

In this paper, we provide a new (proportional) 2-tuple fuzzy linguistic representation model for computing with words (CW), which is based on the concept of "symbolic proportion." This concept motivates us to represent the linguistic information by means of 2-tuples, which are composed by two proportional linguistic terms. For clarity and generality, we first study proportional 2-tuples under ordinal contexts. Then, under linguistic contexts and based on canonical characteristic values (CCVs) of linguistic labels, we define many aggregation operators to handle proportional 2-tuple linguistic information in a computational stage for CW without any loss of information. Our approach for this proportional 2-tuple fuzzy linguistic representation model deals with linguistic labels, which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having "equal distance" between them. Moreover, this new model not only provides a space to allow a "continuous" interpolation of a sequence of ordered linguistic labels, but also provides an opportunity to describe the initial linguistic information by members of a "continuous" linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant. Meanwhile, under the assumption of equally informative (which is defined by a condition based on the concept of CCV), we show that our model reduces to Herrera and Mart/spl inodot//spl acute/nez's (translational) 2-tuple fuzzy linguistic representation model.
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paper_title: An Overview of Computing with Words using Label Semantics

paper_content:

This chapter will give an overview of the label semantics framework for computing with words. Label semantics is an alternative methodology that models linguistic labels in terms of label descriptions, appropriateness measures and mass assignments. It has a clear operational semantics and is straightforward to integrate with other uncertainty formalisms. In the chapter we will introduce the theory of label semantics, discuss its compatibility with a functional calculus and show how it can be used to infer both probabilistic and possibilistic information from linguistic assertions.
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paper_title: A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

paper_content:

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.
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paper_title: Consistency and consensus measures for linguistic preference relations based on distribution assessments

paper_content:

In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making.
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paper_title: A fuzzy sets based linguistic approach: Theory and applications

paper_content:

Fuzzy sets theory and fuzzy logic constitute the basis for the linguistic approach. Under this approach, variables can assume linguistic values. Each linguistic value is characterized by a label and a meaning. The label is a sentence of a language. The meaning is a fuzzy subset of a universe of discourse. Models, based on this approach, can be constructed to simulate approximate reasoning. The implementation of these models presents two major problems, namely how to associate a label to an unlabelled fuzzy set on the basis of semantic similarity (linguistic approximation) and how to perform arithmetic operations with fuzzy numbers. For each problem a solution is proposed. Two illustrative applications are discussed.
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paper_title: Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-Off Precision and Complexity

paper_content:

The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combinations lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for defining the syntax and semantics of a small subset of calculi of uncertainty operating on a given term set of linguistic statements of likelihood. Each calculus will be defined by specifying a negation, a conjunction and a disjunction operator. Families of Triangular norms and conorms will provide the most general representations of conjunction and disjunction operators. These families provide us with a formalism for defining an infinite number of different calculi of uncertainty. The term set will define the uncertainty granularity, i.e. the finest level of distinction among different quantifications of uncertainty. This granularity will limit the ability to differentiate between two similar operators. Therefore, only a small finite subset of the infinite number of calculi will produce notably different results. This result is illustrated by an experiment where nine different calculi of uncertainty are used with three term sets containing five, nine, and thirteen elements, respectively.
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paper_title: On aggregating uncertain information by type-2 OWA operators for soft decision making

paper_content:

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type-2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets. A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc.
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paper_title: On aggregation operations of linguistic labels

paper_content:

This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples. © 1993 John Wiley Sons, Inc.
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paper_title: Computing with Words in Decision support Systems: An overview on Models and Applications

paper_content:

Decision making is inherent to mankind, as human beings daily face situations in which they should choose among different alternatives by means of reasoning and mental processes. Many of these decision problems are under uncertain environments with vague and imprecise information. This type of information is usually modelled by linguistic information because of the common use of language by the experts involved in the given decision situations, originating linguistic decision making. The use of linguistic information in decision making demands processes of Computing with Words to solve the related decision problems. Different methodologies and approaches have been proposed to accomplish such processes in an accurate and interpretable way. The good performance of linguistic computing dealing with uncertainty has caused a spread use of it in different types of decision based applications. This paper overviews the more significant and extended linguistic computing models due to its key role in linguistic decision making and a wide range of the most recent applications of linguistic decision support models.
---
paper_title: Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets

paper_content:

The focus of this paper is the linguistic weighted average (LWA), where the weights are always words modeled as interval type-2 fuzzy sets (IT2 FSs), and the attributes may also (but do not have to) be words modeled as IT2 FSs; consequently, the output of the LWA is an IT2 FS. The LWA can be viewed as a generalization of the fuzzy weighted average (FWA) where the type-1 fuzzy inputs are replaced by IT2 FSs. This paper presents the theory, algorithms, and an application of the LWA. It is shown that finding the LWA can be decomposed into finding two FWAs. Since the LWA can model more uncertainties, it should have wide applications in distributed and hierarchical decision-making.
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paper_title: An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges

paper_content:

Many real world problems need to deal with uncertainty, therefore the management of such uncertainty is usually a big challenge. Hence, different proposals to tackle and manage the uncertainty have been developed. Probabilistic models are quite common, but when the uncertainty is not probabilistic in nature other models have arisen such as fuzzy logic and the fuzzy linguistic approach. The use of linguistic information to model and manage uncertainty has given good results and implies the accomplishment of processes of computing with words. A bird's eye view in the recent specialized literature about linguistic decision making, computing with words, linguistic computing models and their applications shows that the 2-tuple linguistic representation model [44] has been widely-used in the topic during the last decade. This use is because of reasons such as, its accuracy, its usefulness for improving linguistic solving processes in different applications, its interpretability, its ease managing of complex frameworks in which linguistic information is included and so forth. Therefore, after a decade of extensive and intensive successful use of this model in computing with words for different fields, it is the right moment to overview the model, its extensions, specific methodologies, applications and discuss challenges in the topic.
---
paper_title: The 2-tuple Linguistic Model: Computing with Words in Decision Making

paper_content:

This book examines one of the more common and wide-spread methodologies to deal with uncertainty in real-world decision making problems, the computing with words paradigm, and the fuzzy linguistic approach. The 2-tuple linguistic model is the most popular methodology for computing with words (CWW), because it improves the accuracy of the linguistic computations and keeps the interpretability of the results. The authors provide a thorough review of the specialized literature in CWW and highlight the rapid growth and applicability of the 2-tuple linguistic model. They explore the foundations and methodologies for CWW in complex frameworks and extensions. The book introduces the software FLINTSTONES that provides tools for solving linguistic decision problems based on the 2-tuple linguistic model. Professionals and researchers working in the field of classification or fuzzy sets and systems will find The 2-tuple Linguistic Model: Computing with Words in Decision Making a valuable resource. Undergraduate and postdoctoral students studying computer science and statistics will also find this book a useful study guide.
---
paper_title: Environmental impact assessment using the evidential reasoning approach

paper_content:

Environmental impact assessment (EIA) problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments, which inevitably involve various types of uncertainties such as ignorance and fuzziness. So, EIA problems need to be modelled and analysed using methods that can handle uncertainties. The evidential reasoning (ER) approach provides such a modelling framework and analysis method. In this paper the ER approach will be applied to conduct EIA analysis for the first time. The environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive. All assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, is modelled using a unified framework of a belief structure. The original ER approach with a recursive ER algorithm will be introduced and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed such as in optimisation problems. The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy. A numerical example and its modified version are studied to illustrate the detailed implementation process of the ER approach and demonstrate its potential applications in EIA.
---
paper_title: Computing with words to assess the sustainability of renewable energy options

paper_content:

Appraising the Renewable Energy Sources (RES) options' contribution to Sustainable Development (SD) is a complex task, considering the different aspects of SD the imprecision and uncertainty of the related information as well as the qualitative aspects embodied, that cannot be represented by numerical values. The objective of the paper is to show how energy policy objectives towards SD and RES options are related and assessed using linguistic variables. The presented method extends the numerical multicriteria method TOPSIS for processing linguistic information, eliminating in parallel the loss of information caused by the approximation procedures and the ambiguity of the fuzzy ranking method's selection. Moreover, the application of the method's computerized software to the RES interventions proposed in the Hellenic National Action Plan for Greenhouse Gases is presented and discussed.
---
paper_title: Hesitant Fuzzy Linguistic Term Sets for Decision Making

paper_content:

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate between several values to assess an indicator, alternative, variable, etc. Hesitant fuzzy sets suit the modeling of quantitative settings; however, similar situations may occur in qualitative settings so that experts think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. Then, a multicriteria linguistic decision-making model is presented in which experts provide their assessments by eliciting linguistic expressions. This decision model manages such linguistic expressions by means of its representation using hesitant fuzzy linguistic term sets.
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paper_title: A 360-degree performance appraisal model dealing with heterogeneous information and dependent criteria

paper_content:

A 360-degree performance appraisal process is used as a tool that provides an evaluation about employees' performance. It is based on the opinion of different groups of reviewers who socialize with evaluated employees. Multiple criteria are considered in performance appraisal that may have different nature and usually present uncertainty. Therefore, it seems necessary and appropriate to provide a heterogeneous framework adapted to the nature of such criteria. In this context, criteria can be assessed by reviewers, according to their background and degree of knowledge about evaluated employees. Furthermore, Human Resources Department demands the modeling and managing of the interaction among the evaluated criteria, as well as reviewers relevances to ensure an effective aggregation process of the information, providing interpretable, understandable and correct assessments. In this paper, we present an integrated model for 360-degree performance appraisal that can manage heterogeneous information and computes a final linguistic evaluation for each employee, applying an effective aggregation that considers the interaction among criteria and reviewers relevance by means of weights. We also present a real case study to show the usefulness and effectiveness of the proposed model.
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paper_title: A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

paper_content:

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.
---
paper_title: Consistency and consensus measures for linguistic preference relations based on distribution assessments

paper_content:

In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making.
---
paper_title: A new version of 2-tuple fuzzy linguistic representation model for computing with words

paper_content:

In this paper, we provide a new (proportional) 2-tuple fuzzy linguistic representation model for computing with words (CW), which is based on the concept of "symbolic proportion." This concept motivates us to represent the linguistic information by means of 2-tuples, which are composed by two proportional linguistic terms. For clarity and generality, we first study proportional 2-tuples under ordinal contexts. Then, under linguistic contexts and based on canonical characteristic values (CCVs) of linguistic labels, we define many aggregation operators to handle proportional 2-tuple linguistic information in a computational stage for CW without any loss of information. Our approach for this proportional 2-tuple fuzzy linguistic representation model deals with linguistic labels, which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having "equal distance" between them. Moreover, this new model not only provides a space to allow a "continuous" interpolation of a sequence of ordered linguistic labels, but also provides an opportunity to describe the initial linguistic information by members of a "continuous" linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant. Meanwhile, under the assumption of equally informative (which is defined by a condition based on the concept of CCV), we show that our model reduces to Herrera and Mart/spl inodot//spl acute/nez's (translational) 2-tuple fuzzy linguistic representation model.
---
paper_title: Environmental impact assessment using the evidential reasoning approach

paper_content:

Environmental impact assessment (EIA) problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments, which inevitably involve various types of uncertainties such as ignorance and fuzziness. So, EIA problems need to be modelled and analysed using methods that can handle uncertainties. The evidential reasoning (ER) approach provides such a modelling framework and analysis method. In this paper the ER approach will be applied to conduct EIA analysis for the first time. The environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive. All assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, is modelled using a unified framework of a belief structure. The original ER approach with a recursive ER algorithm will be introduced and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed such as in optimisation problems. The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy. A numerical example and its modified version are studied to illustrate the detailed implementation process of the ER approach and demonstrate its potential applications in EIA.
---
paper_title: A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making

paper_content:

Decision making is a process common to human beings. The uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision. The recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguistic terms to provide their assessments. The use of linguistic intervals whose results lose their initial fuzzy representation was introduced to facilitate the computing processes in which such expressions are used. The aim of this paper is to present a new representation of the hesitant fuzzy linguistic term sets by means of a fuzzy envelope to carry out the computing with words processes. This new fuzzy envelope can be directly applied to fuzzy multicriteria decision making models. An illustrative example of its application to a supplier selection problem through the use of fuzzy TOPSIS is presented.
---
paper_title: The 2-tuple Linguistic Model: Computing with Words in Decision Making

paper_content:

This book examines one of the more common and wide-spread methodologies to deal with uncertainty in real-world decision making problems, the computing with words paradigm, and the fuzzy linguistic approach. The 2-tuple linguistic model is the most popular methodology for computing with words (CWW), because it improves the accuracy of the linguistic computations and keeps the interpretability of the results. The authors provide a thorough review of the specialized literature in CWW and highlight the rapid growth and applicability of the 2-tuple linguistic model. They explore the foundations and methodologies for CWW in complex frameworks and extensions. The book introduces the software FLINTSTONES that provides tools for solving linguistic decision problems based on the 2-tuple linguistic model. Professionals and researchers working in the field of classification or fuzzy sets and systems will find The 2-tuple Linguistic Model: Computing with Words in Decision Making a valuable resource. Undergraduate and postdoctoral students studying computer science and statistics will also find this book a useful study guide.
---
paper_title: A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

paper_content:

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.
---
paper_title: A fusion approach for managing multi-granularity linguistic term sets in decision making

paper_content:

The aim of this paper is to present a fusion approach of multi-granularity linguistic information for managing information assessed in different linguistic term sets (multi-granularity linguistic term sets) together with its application in a decision making problem with multiple information sources, assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and/or semantic. In this context, a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives. First, the fusion of the multi-granularity linguistic performance values is carried out in order to obtain collective performance evaluations. In this step, on the one hand, the multi-granularity linguistic information is made uniform using a linguistic term set as the uniform representation base, the basic linguistic term set. On the other hand, the collective performance evaluations of the alternatives are obtained by means of an aggregation operator, being fuzzy sets on the basic linguistic term set. Second, the choice of the best alternative(s) from the collective performance evaluations is performed. To do that, a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of Possibility Theory, applied to fuzzy sets on the basic linguistic term set. Then, a choice degree may be applied on the preference relation in order to rank the alternatives.
---
paper_title: Environmental impact assessment using the evidential reasoning approach

paper_content:

Environmental impact assessment (EIA) problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments, which inevitably involve various types of uncertainties such as ignorance and fuzziness. So, EIA problems need to be modelled and analysed using methods that can handle uncertainties. The evidential reasoning (ER) approach provides such a modelling framework and analysis method. In this paper the ER approach will be applied to conduct EIA analysis for the first time. The environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive. All assessment information, quantitative or qualitative, complete or incomplete, and precise or imprecise, is modelled using a unified framework of a belief structure. The original ER approach with a recursive ER algorithm will be introduced and a new analytical ER algorithm will be investigated which provides a means for using the ER approach in decision situations where an explicit ER aggregation function is needed such as in optimisation problems. The ER approach will be used to aggregate multiple environmental factors, resulting in an aggregated distributed assessment for each alternative policy. A numerical example and its modified version are studied to illustrate the detailed implementation process of the ER approach and demonstrate its potential applications in EIA.
---
paper_title: A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

paper_content:

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.
---
paper_title: Consistency and consensus measures for linguistic preference relations based on distribution assessments

paper_content:

In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making.
---
paper_title: Hesitant Fuzzy Linguistic Term Sets for Decision Making

paper_content:

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate between several values to assess an indicator, alternative, variable, etc. Hesitant fuzzy sets suit the modeling of quantitative settings; however, similar situations may occur in qualitative settings so that experts think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. Then, a multicriteria linguistic decision-making model is presented in which experts provide their assessments by eliciting linguistic expressions. This decision model manages such linguistic expressions by means of its representation using hesitant fuzzy linguistic term sets.
---
paper_title: A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

paper_content:

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.
---
paper_title: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making

paper_content:

AbstractGroup decision making problems which organize a group of experts to evaluate a set of alternatives with respect to several criteria are commonly discussed recently. Hesitant fuzzy linguistic term sets, characterized by a set of consecutive linguistic terms, act as a new model for qualitative settings where experts think of several possible linguistic values or richer expressions than a single term. When evaluating an indicator, alternative or variable in group decision making, however, linguistic terms involved in an expression derived by the group may be not always consecutive. Therefore, we generalize hesitant fuzzy linguistic term sets by enabling any non-consecutive linguistic terms in them, and refer to as extended hesitant fuzzy linguistic term sets (EHFLTSs). EHFLTSs can be constructed by the union of hesitant fuzzy linguistic term sets given by individual expert. As owning more desirable mathematical properties, EHFLTSs are flexible for develop complex decision model. Some basic operation ...
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paper_title: A multi-granular linguistic model to evaluate the suitability of installing an ERP system

paper_content:

The use of Enterprise Resource Planning (ERP) has shown clearly useful and economically profitable in most very large organizations which manage a great deal of data in their information systems. Nevertheless, the decision of installing an ERP system is not easy and it depends on the size, future profits and other features of the companies. The assessments of the parameters (features, aspects) used to evaluate the suitability of the ERP may be vague and imprecise because they are usually perceptions of the experts. We propose the use of linguistic information to assess these parameters due to the fact that it is very suitable to model and manage human perceptions. In addition, it may be that each expert has a different knowledge about each parameter and prefers to express his/her preferences in his/her own linguistic term set. Therefore, to manage the evaluation problem of installing an ERP, in this contribution we present a multi-granular linguistic evaluation model that covers these necessities.
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paper_title: The 2-tuple Linguistic Model: Computing with Words in Decision Making

paper_content:

This book examines one of the more common and wide-spread methodologies to deal with uncertainty in real-world decision making problems, the computing with words paradigm, and the fuzzy linguistic approach. The 2-tuple linguistic model is the most popular methodology for computing with words (CWW), because it improves the accuracy of the linguistic computations and keeps the interpretability of the results. The authors provide a thorough review of the specialized literature in CWW and highlight the rapid growth and applicability of the 2-tuple linguistic model. They explore the foundations and methodologies for CWW in complex frameworks and extensions. The book introduces the software FLINTSTONES that provides tools for solving linguistic decision problems based on the 2-tuple linguistic model. Professionals and researchers working in the field of classification or fuzzy sets and systems will find The 2-tuple Linguistic Model: Computing with Words in Decision Making a valuable resource. Undergraduate and postdoctoral students studying computer science and statistics will also find this book a useful study guide.
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Title: An Overview on Fuzzy Modelling of Complex Linguistic Preferences in Decision Making

Section 1: Introduction
Description 1: Introduce the challenges and requirements in decision making processes, emphasizing the need for fuzzy linguistic approaches to handle uncertainty and vagueness in complex decision problems.

Section 2: Decision Making and Linguistic Information
Description 2: Provide a brief review of the use of fuzzy linguistic information in decision making, explaining necessary concepts to understand fuzzy based approaches.

Section 3: Fuzzy Linguistic Approach
Description 3: Discuss the fuzzy linguistic approach based on fuzzy set theory, covering the key concepts and components involved in modeling linguistic information.

Section 4: Linguistic Decision Making Solving Scheme
Description 4: Outline the steps involved in the linguistic decision making solving scheme, including selecting linguistic term sets, aggregation operators, and performing aggregation and exploitation phases.

Section 5: Linguistic Computing Models
Description 5: Review different linguistic computing models developed to operate with linguistic information in decision making processes.

Section 6: Modelling Complex Linguistic Preferences
Description 6: Provide an overview of various proposals for modeling complex linguistic preferences, highlighting the construction and computational models used for these expressions.

Section 7: Proportional 2-tuple Linguistic Model
Description 7: Describe the proportional 2-tuple linguistic model, its representation, computational model, and relevant aggregation operators.

Section 8: Linguistic Model Based on Fuzzy Relation
Description 8: Introduce the linguistic model based on fuzzy relation, explaining its expressions, computational model, and application in decision making.

Section 9: A Fuzzy-set Approach to Treat Determinacy and Consistency of Linguistic Terms
Description 9: Discuss the approach for treating determinacy and consistency of linguistic terms, including the computational model and synthesis of comments.

Section 10: Linguistic Distribution
Description 10: Explain the concept of linguistic distribution, its representation, comparison, and aggregation operators.

Section 11: Complex Linguistic Expressions Based on Hesitant Fuzzy Linguistic Term Sets
Description 11: Present the complex linguistic expressions based on Hesitant Fuzzy Linguistic Term Sets (HFLTS), including the generation and flexibility of comparative expressions.

Section 12: Challenges and Future in Modelling Complex Linguistic Preferences
Description 12: Outline the challenges and potential future research directions in modelling complex linguistic preferences, emphasizing the need for flexible and hybrid modelling approaches.

Section 13: Conclusions
Description 13: Summarize the key insights from the overview, highlighting the necessity of flexible and complex linguistic expressions in decision making and future research challenges.