A New Model for Deriving the Priority Weights from Hesitant Triangular Fuzzy Preference Relations

Yuan Liu,Zhangyan Zhao,Zhanwen Wu,Gongtian Shen

doi:10.1155/2019/8586592

Abstract

Fuzzy preference relation is a common tool to express the uncertain preference information of decision maker in the process of decision making. However, the traditional fuzzy preference relation will fail under hesitant fuzzy environment as the membership has a single value. In addition, it is very difficult to obtain the precise membership values. Therefore, a new model of fuzzy preference relation is proposed in this paper. Firstly, the concept of hesitant triangular fuzzy preference relation is defined and its properties are investigated based on the concepts of hesitant fuzzy set, hesitant triangular fuzzy set, fuzzy preference relation, and hesitant fuzzy preference relation. Then, the steps of applying this novel model are offered for the case of determining the weights of failure modes. Finally, an example is used to illustrate the proposed model.

Highlights

Having received extensive attention in the last few decades, preference relation is a widely used and effective tool to express the preference of decision makers over the alternatives in decision making [1, 2]
Despite the superiority of interval-valued intuitionistic fuzzy sets (IVIFSs) in describing fuzziness and uncertainty compared with other preference relations, IVIFSs are not applicable to the situation of several possible preference values commonly seen in many practical problems
In order to cluster the massive evaluation information provided by different experts, Chen and Xu [25] proposed a series of correlation coefficient formulae for hesitant fuzzy sets (HFSs) and applied them to calculating the degrees of correlation among HFSs

Summary

Introduction

Having received extensive attention in the last few decades, preference relation is a widely used and effective tool to express the preference of decision makers over the alternatives in decision making [1, 2]. Despite the superiority of IVIFSs in describing fuzziness and uncertainty compared with other preference relations, IVIFSs are not applicable to the situation of several possible preference values commonly seen in many practical problems For this limitation, Torra and Narukawa [20, 21] introduced the hesitant fuzzy sets (HFSs), a novel and recent extension of fuzzy sets. In order to cluster the massive evaluation information provided by different experts, Chen and Xu [25] proposed a series of correlation coefficient formulae for HFSs and applied them to calculating the degrees of correlation among HFSs. Rodrıguez, R.M., et al [26] made an overview on hesitant fuzzy sets including concept, extension, aggregation operators, measures, and applications like decision making, evaluation, and clustering. For further applications of HFLTSs to decision making, Zhu and Xu [31] developed a concept of hesitant fuzzy linguistic preference relations (HFLPRs) as a tool to collect and present the decision makers' preferences.

Preliminaries

Proposed Methodology

Case Illustration

Conclusion