Interval-Valued Hesitant Fuzzy Linguistic Multiattribute Decision-Making Method Based on Three-Parameter Heronian Mean Operators

Wang Juan,Li Qiang,Feng Feng

doi:10.1155/2021/3634895

Abstract

Numerous variants have been proposed for sets of linguistic terms and the interval-valued hesitant fuzzy set (IVHFS). In particular, the interval-valued hesitant fuzzy linguistic set (IVHFLS) is more suitable for defining the hesitancy and inconsistency inherent in the human cognitive processes of decision making. A key aggregation operator is Heronian mean (HM), based on which the correlation among aggregated arguments can be captured. However, the existing HM operators partially overlook the correlation among more than two arguments and lack the properties of idempotency and reducibility. In this work, the limitations of HM operators are first analyzed. Then, two new HM variants are introduced: three-parameter weighted Heronian mean (TPWHM) and three-parameter weighted geometric Heronian mean (TPWGHM). Thus, the reducibility, idempotency, monotonicity, and boundedness properties are proven for the two computational procedures, and unique situations are mentioned. Furthermore, two more elaborate operators are also introduced which are called the interval-valued hesitant fuzzy linguistic TPWHM (IVHFLTPWHM) and the interval-valued hesitant fuzzy linguistic TPWGHM (IVHFLTPWGHM). The main properties, as well as unique situations of these two computational procedures, are discussed. Finally, the introduced methods are clarified by illustrative examples. In addition, the parameter effects on the decision-making outcomes are discussed and comparisons with other reference methods are made.

Highlights

MADM naturally arises in numerous practical applications, including ones in supplier selection [1], medical diagnosis [2], investment project selection [3], and so on
We introduce two novel Heronian mean (HM) operators, namely, the three-parameter weighted HM (TPWHM) and the three-parameter weighted geometric HM (TPWGHM), which are shown to be reducible, idempotent, monotone, and bounded and they do not suffer from deficiencies that are already mentioned. e other sections of the manuscript are organized as follows
We show that the IVHFLTPWHM operator is idempotent, monotone, and bounded

Summary

Introduction

MADM naturally arises in numerous practical applications, including ones in supplier selection [1], medical diagnosis [2], investment project selection [3], and so on. Real decision-making problems are complicated by stringent requirements and constraints, including primarily the ability to process fuzzy and vague information. Under these constraints, many methods have been suggested for expressing fuzzy and vague information. Farhadinia [12, 13] proposed an intervalvalued hesitant fuzzy set (IVHFS) and multiple measuring tools. Xu [18] and Akram et al [19] presented variants of the TOPSIS method within the frameworks of the conventional and neutrosophic hesitant fuzzy sets. Zhu et al [20] developed the operators of the hesitant fuzzy geometric Bonferroni mean (HFGBM) as well as the hesitant fuzzy Choquet geometric Bonferroni

Methods

Results

Conclusion