HESITANT FUZZY MULTI-CRITERIA DECISION MAKING METHODS BASED ON HERONIAN MEAN

Dejian Yu

doi:10.3846/20294913.2015.1072755

Abstract

Among several extensions of fuzzy set theory, the concept introduced by Torra and Narukawa (2009) in defining hesitant fuzzy set is interesting and practical. In this paper we introduce and study new methods for dealing with MCDM (multi-criteria decision making) problems under the hesitant fuzzy environment. First, we propose and discuss the notion of hesitant fuzzy Heronian mean operators. By using these operators, we can portray the relationship of the criteria effectively. Then, the numerical examples are provided and comparative analyses with other aggregation operators are not neglected. Furthermore, the weighted forms of the hesitant fuzzy Heronian mean operators are defined for MCDM problem, based on which, new MCDM methods are proposed. The MCDM methods presented in this paper can provide an effective manner to assist the decision maker in making his/her decision. An example about dormitory construction projection selection is given to show the effectiveness of the proposed method.

Highlights

Torra and Narukawa (2009) developed the concept of hesitant fuzzy set (HFS), which is an extension of fuzzy set, characterized by the membership function expressed by a set of some possible values between [0,1]
We have researched new hesitant fuzzy MCDM methods, and we have applied them in dormitory construction projection selection problem
We have put forwarded some operators for hesitant fuzzy elements (HFEs), such as hesitant fuzzy Heronian mean operator (HFHM), hesitant fuzzy geometric Heronian mean operator (HFGHM), hesitant fuzzy weighted Heronian mean operator (HFWHM) and hesitant fuzzy weighted geometric Heronian mean operator (HFWGHM) operators

Summary

Introduction

Torra and Narukawa (2009) developed the concept of hesitant fuzzy set (HFS), which is an extension of fuzzy set, characterized by the membership function expressed by a set of some possible values between [0,1]. With the aid of quasi-arithmetic means, Xia et al (2013) introduced the generalized form of hesitant fuzzy aggregation operators. Zhu et al (2012) introduced some objective correlated aggregation operators called geometric Bonferroni means operators and hesitant fuzzy Bonferroni means operators respectively. A comparative example is presented for finding correlations with hesitant fuzzy BM operators (Zhu, Xu 2013b; Zhu et al 2012) and shows the applicability of the proposed MCDM approach. Hesitant fuzzy multi-criteria decision making methods based on Heronian mean

Some basic concepts

Hesitant fuzzy MCDM based on weighted Heronian mean operators

Conclusions