Two Hesitant Multiplicative Decision-Making Algorithms and Their Application to Fog-Haze Factor Assessment Problem

Lidan Pei,Feifei Jin

doi:10.3390/a11100154

Abstract

Hesitant multiplicative preference relation (HMPR) is a useful tool to cope with the problems in which the experts utilize Saaty’s 1–9 scale to express their preference information over paired comparisons of alternatives. It is known that the lack of acceptable consistency easily leads to inconsistent conclusions, therefore consistency improvement processes and deriving the reliable priority weight vector for alternatives are two significant and challenging issues for hesitant multiplicative information decision-making problems. In this paper, some new concepts are first introduced, including HMPR, consistent HMPR and the consistency index of HMPR. Then, based on the logarithmic least squares model and linear optimization model, two novel automatic iterative algorithms are proposed to enhance the consistency of HMPR and generate the priority weights of HMPR, which are proved to be convergent. In the end, the proposed algorithms are applied to the factors affecting selection of fog-haze weather. The comparative analysis shows that the decision-making process in our algorithms would be more straight-forward and efficient.

Highlights

In a group decision making (GDM) situation, the decision makers (DMs) are usually required to select the desirable alternative(s) from a collection of alternatives
Xia and Xu [18] introduced the concepts of hesitant fuzzy preference relation (HFPR) and hesitant multiplicative preference relation (HMPR) and studied their properties, which are followed by the construction of some methods of group decision making (GDM)
Assume that P =n×n is an Hesitant multiplicative preference relation (HMPR), w = (w1, w2, · · ·, wn )T is the priority weight vector derived from P satisfying wi > 0, ∀i ∈ N, ∑in=1 wi = 1, the consistency index of P is defined as CI ( P) =

Summary

Introduction

In a group decision making (GDM) situation, the decision makers (DMs) are usually required to select the desirable alternative(s) from a collection of alternatives. Xia and Xu [18] introduced the concepts of hesitant fuzzy preference relation (HFPR) and hesitant multiplicative preference relation (HMPR) and studied their properties, which are followed by the construction of some methods of group decision making (GDM). Pei et al [26] developed an iterative algorithm to adjust the additive consistency of IFLPRs and derive the intuitionistic fuzzy weights for IFLPRs. Based on β-normalization, Zhu et al [27] utilized the optimized parameter to develop a novel approach for inconsistent HFPRs. Under the hesitant fuzzy preference information environment, Zhang et al [28] constructed a decision support model to derive the most desirable alternative. Based on the β-normalization principle, Zhang and Wu [28] investigated a new decision-making model to generate the interval weights of alternatives from HMPRs. with the algorithm in.

Preliminaries

Hesitant Multiplicative Preference Relations and Consistency Index

Consistency Repaired Methods for an HMPR

Numerical Example

Discussions

Conclusions