Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision-Making

Jun Wang,Xiaomin Zhu,Runtong Zhang,Yuping Xing,Borut Buchmeister

doi:10.1155/2018/5087851

Jun Wang, Xiaomin Zhu + Show 3 more

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https://doi.org/10.1155/2018/5087851

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Journal: Complexity	Publication Date: Jun 26, 2018
Citations: 12	License type: CC BY 4.0

Affiliation: Beijing Jiaotong University, University of Maribor

Abstract

The proposed hesitant fuzzy linguistic set (HFLS) is a powerful tool for expressing fuzziness and uncertainty in multiattribute group decision-making (MAGDM). This paper aims to propose novel aggregation operators to fuse hesitant fuzzy linguistic information. First, we briefly recall the notion of HFLS and propose new operations for hesitant fuzzy linguistic elements (HFLEs). Second, considering the Muirhead mean (MM) is a useful aggregation technology that can consider the interrelationship among all aggregated arguments, we extend it to hesitant fuzzy linguistic environment and propose new hesitant fuzzy linguistic aggregation operators, such as the hesitant fuzzy linguistic Muirhead mean (HFLMM) operator, the hesitant fuzzy linguistic dual Muirhead mean (HFLDMM) operator, the hesitant fuzzy linguistic weighted Muirhead mean (HFLMM) operator, and the hesitant fuzzy linguistic weighted dual Muirhead mean (HFLWDMM) operator. These operators can reflect the correlations among all HFLEs. Several desirable properties and special cases of the proposed operators are also studied. Furthermore, we propose a novel approach to MAGDM in a hesitant fuzzy linguistic context based on the proposed operators. Finally, we conduct a numerical experiment to demonstrate the validity of our method. Additionally, we compare our method with others to illustrate its merits and superiorities.

Highlights

multiattribute group decision-making (MAGDM) is an activity that selects the optimal alternative under a set of attributes assessed by a group of decisionmakers
Considering the Muirhead mean (MM) is a useful aggregation technology that can consider the interrelationship among all aggregated arguments, we extend it to hesitant fuzzy linguistic environment and propose new hesitant fuzzy linguistic aggregation operators, such as the hesitant fuzzy linguistic Muirhead mean (HFLMM) operator, the hesitant fuzzy linguistic dual Muirhead mean (HFLDMM) operator, the hesitant fuzzy linguistic weighted Muirhead mean (HFLMM) operator, and the hesitant fuzzy linguistic weighted dual Muirhead mean (HFLWDMM) operator
The contribution of this paper is that we propose new operators for aggregating hesitant fuzzy linguistic information that can capture the interrelationship among all hesitant fuzzy linguistic elements (HFLEs)

Summary

Introduction

MAGDM is an activity that selects the optimal alternative under a set of attributes assessed by a group of decisionmakers. Owing to the increased complexity in decisionmaking, one of the difficulties in practical MAGDM problems is representing attribute values in fuzzy and vague decisionmaking environments. These fuzzy sets have been successfully applied to decision-making [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] These tools are unsuitable to cope with circumstances in which decision-makers are hesitant between a few different values when determining membership degree.

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