Additively Consistent Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Application to Group Decision Making

Hua Zhuang

doi:10.3390/info9100260

Abstract

This paper aims to propose an innovative approach to group decision making (GDM) with interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). First, an IVIFPR is proposed based on the additive consistency of an interval-valued fuzzy preference relation (IVFPR). Then, two mathematical or adjusted programming models are established to extract two special consistent IVFPRs. In order to derive the priority weight of an IVIFPR, after taking the two special IVFPRs into consideration, a linear optimization model is constructed by minimizing the deviations between individual judgments and between the width degrees of the interval priority weights. For GDM with IVIFPRs, the decision makers’ weights are generated by combining the adjusted subjective weights with the objective weights. Subsequently, using an IVIF-weighted averaging operator, the collective IVIFPR is obtained and utilized to derive the IVIF priority weights. Finally, a practical example of a supplier selection is analyzed to demonstrate the application of the proposed method.

Highlights

In group decision making (GDM), decision makers (DMs) are usually required to provide their judgment on various alternatives using preference relations
The three types of preference relations in which the elements are described by crisp numerical numbers are multiplicative preference relations (MPRs) [1], reciprocal preference relations (RPRs) [2], and linguistic fuzzy preference relations (LFPRs) [3]
The additive consistency concept of an IVIFPR has been defined according to the additive transitivity of an interval-valued fuzzy preference relation (IVFPR)

Summary

Introduction

In group decision making (GDM), decision makers (DMs) are usually required to provide their judgment on various alternatives using preference relations. The three types of preference relations in which the elements are described by crisp numerical numbers are multiplicative preference relations (MPRs) [1], reciprocal preference relations (RPRs) [2], and linguistic fuzzy preference relations (LFPRs) [3]. Due to the practical uncertainty and vagueness of decision problems, DMs may find it difficult to provide pairwise comparison judgments with crisp numerical numbers for the alternatives. The intuitionistic fuzzy set (IFS) proposed by Atanassov [4] is a powerful tool to handle this problem, which is characterized by a membership and nonmembership degree. Atanassov and Gargov [5] used the IFS to propose an interval-valued intuitionistic fuzzy set (IVIFS). The interval-valued fuzzy preference relation (IVFPR) [6,7,8,9] and the interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPR) [10,11,12,13,14] appeared in succession

Objectives

Methods

Conclusion