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2017 | Book

Hesitant Fuzzy Methods for Multiple Criteria Decision Analysis

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About this book

The book offers a comprehensive introduction to methods for solving multiple criteria decision making and group decision making problems with hesitant fuzzy information. It reports on the authors’ latest research, as well as on others’ research, providing readers with a complete set of decision making tools, such as hesitant fuzzy TOPSIS, hesitant fuzzy TODIM, hesitant fuzzy LINMAP, hesitant fuzzy QUALIFEX, and the deviation modeling approach with heterogeneous fuzzy information. The main focus is on decision making problems in which the criteria values and/or the weights of criteria are not expressed in crisp numbers but are more suitable to be denoted as hesitant fuzzy elements. The largest part of the book is devoted to new methods recently developed by the authors to solve decision making problems in situations where the available information is vague or hesitant. These methods are presented in detail, together with their application to different type of decision-making problems. All in all, the book represents a valuable reference guide for graduate students and researchers in the both fields of fuzzy logic and decision making.

Table of Contents

Frontmatter
Chapter 1. Hesitant Fuzzy Multiple Criteria Decision Analysis Based on TOPSIS
Abstract
HFE which allows the membership degree of an element to a set represented by several possible values is a powerful tool to describe and deal with uncertain data. This chapter develops the decision making approach based on TOPSIS and the maximizing deviation model for solving MCDM problems in which the evaluation information provided by the decision maker is expressed in HFEs and the information about criteria weights is incomplete. There are two key issues being addressed in this approach. The first one is to establish an optimization model based on the maximizing deviation method, which can be used to determine the weights of criteria. The second one is to calculate the revised closeness index of each alternative to the hesitant fuzzy PIS. The considered alternatives are ranked according to the revised closeness indices of alternatives and the most desirable one is selected. An important advantage of this proposed method is its ability to relieve the influence of subjectivity of the decision maker concerning the weights of criteria and at the same time to remain the original decision information sufficiently. Additionally, the extended results in the interval-valued hesitant fuzzy situations are also pointed out.
Xiaolu Zhang, Zeshui Xu
Chapter 2. Hesitant Fuzzy Multiple Criteria Decision Analysis Based on TODIM
Abstract
The TODIM is a valuable technique for solving classical MCDM problems in case of considering the decision maker’s psychological behavior. One main goal of this chapter is to introduce the measured functions-based hesitant fuzzy TODIM technique to deal with the behavioral MCDM problem under hesitant fuzzy environments. The main advantages of this technique are that (1) it can handle the MCDM problems in which the ratings of alternatives with respect to each criterion are represented by HFEs or IVHFEs and (2) it can take the decision maker’s psychological behavior into account. Another aim of this chapter is to present the hesitant trapezoidal fuzzy TODIM method with a closeness index-based ranking approach to handle MCGDM problems in which decision data is expressed as comparative linguistic expressions based on HTrFNs. This proposed method first transforms comparative linguistic expressions into HTrFNs for carrying out computing with word processes. Then, a closeness index-based ranking method is proposed for comparing the magnitude of HTrFNs. By using such a ranking method, the dominance values of alternatives over others for each expert are calculated. Next, a nonlinear programming model is established to derive the dominance values of alternatives over others for the group and correspondingly the optimal ranking order of alternatives is determined.
Xiaolu Zhang, Zeshui Xu
Chapter 3. Hesitant Fuzzy Multiple Criteria Decision Analysis Based on QUALIFLEX
Abstract
The QUALIFLEX is a very useful outranking method to deal simultaneously with the cardinal and ordinal information in decision making process. The purpose of this chapter is to develop the hesitant fuzzy QUALIFLEX with a signed distance-based comparison method for handling MCDM problems in which both the assessments of alternatives on criteria and the weights of criteria are expressed by HFEs. In this chapter, we propose the novel concept of hesitancy index for the HFE to measure the degree of hesitancy of the decision-maker or the decision organization. By taking their hesitancy indices into account, we present a signed distance-based ranking method to compare the magnitude of HFEs. By adopting such a comparison approach, the hesitant fuzzy QUALIFLEX technique is developed. Compared with the hesitant fuzzy ELECTRE method, to handle the MCDM problems where the number of criteria markedly exceeds the number of alternatives the developed technique does not require the complicated computation procedures but still yields a reasonable and credible solution. Finally, the developed technique is extended to manage the heterogeneous information including real numbers, interval numbers, TFNs, IFNs, and HFEs.
Xiaolu Zhang, Zeshui Xu
Chapter 4. Hesitant Fuzzy Multiple Criteria Decision Analysis Based on LINMAP
Abstract
The LINMAP technique is one of the most representative methods for handling the MCDM or MCGDM problems with respect to the preference information over alternatives. This chapter utilizes the main structure of LINMAP to develop the hesitant fuzzy group LINMAP technique with interval programming model and the hesitant fuzzy programming model-based LINMAP technique. The former is mainly used to solve the MCGDM problems in which the ratings of alternatives with respect to criteria are taken as HFEs, and all pair-wise comparison judgments are represented by interval numbers. While the latter is mainly utilized to address the MCDM problems with incomplete weight information in which the ratings of alternatives with each criterion are taken as HFEs and the incomplete judgments on pair-wise comparisons of alternatives with hesitant degrees are also represented by HFEs. The main contributions of this chapter are that (1) the developed techniques not only can take sufficiently into account the experts’ hesitancy in expressing their assessment information for criteria values by using HFEs but also can simultaneously consider the uncertainty of preference information over alternatives by using interval numbers or HFEs; (2) the concept of hesitant fuzzy programming model in which both the objective function and the constraints’ coefficients take the form of HFEs has been proposed, and an effective technique to solve this sort of model is developed; (3) the bi-objective programming model has been constructed to address the issues of incomplete and inconsistent weights of the criteria.
Xiaolu Zhang, Zeshui Xu
Chapter 5. Consensus Model-Based Hesitant Fuzzy Multiple Criteria Group Decision Analysis
Abstract
The MCGDM is an important research topic in decision theory. Many useful methods have been proposed to solve various MCGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the hesitant fuzzy situations. The purpose of this chapter is to develop a consensus model-based hesitant fuzzy group decision making method to handle hesitant fuzzy MCGDM problems by simultaneously taking into account such two aspects of hesitant fuzzy decision data. Firstly, an ordinal consensus index is presented for measuring the consensus among individual experts’ opinions from the perspective of the ranking of decision information. Then, a cardinal consensus index is presented for measuring the consensus among individual experts’ opinions from the perspective of the magnitude of decision information. Afterwards, a linear programming model to derive the weights of experts is constructed according to the idea that the expert with a larger consensus should be assigned a larger weight. Finally, the relative closeness indices of alternatives are determined and the ranking of alternatives is identified.
Xiaolu Zhang, Zeshui Xu
Chapter 6. Heterogeneous Multiple Criteria Group Decision Analysis
Abstract
The purpose of this chapter is to develop the deviation modeling method to deal with the heterogeneous MCGDM problems with incomplete weight information in which the decision information is expressed as real numbers, interval numbers, linguistic variables, IFNs, HFEs and HFLTSs. The most characteristic of the deviation modeling method is that it does not unify the heterogeneous information but directly calculates the distances to the PIS and NIS. Compared with Li et al. (2010b)’s method, the advantages of the developed method are that (1) it can accommodate more complicated decision data, including IFNs, HFEs and HFLTSs; (2) it utilizes the maximization deviation model to determine objectively the weights of the criteria for each expert, which avoids the subjective randomness of selecting the weights; (3) it can consider fully the consistency between the opinions of the individual experts and the group, thus the final decision results derived by it are more persuasive.
Xiaolu Zhang, Zeshui Xu
Metadata
Title
Hesitant Fuzzy Methods for Multiple Criteria Decision Analysis
Authors
Xiaolu Zhang
Zeshui Xu
Copyright Year
2017
Electronic ISBN
978-3-319-42001-1
Print ISBN
978-3-319-42000-4
DOI
https://doi.org/10.1007/978-3-319-42001-1

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