Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making

Zhiming Zhang

doi:10.1155/2013/670285

Abstract

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modelling people’s hesitancy in daily life. In this paper, we extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers. The aim of this paper is to develop a series of aggregation operators for interval-valued intuitionistic hesitant fuzzy information. Then, some desired properties of the developed operators are studied, and the relationships among these operators are discussed. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision-making with interval-valued intuitionistic hesitant fuzzy information. Finally, a numerical example is provided to illustrate the application of the developed approach.

Highlights

In many practical problems, when defining the membership degree of an element, the difficulty of establishing the membership degree is not because we have a margin of error or some possibility distribution on the possibility values, but because we have several possible numerical values
We extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers
We look at some special cases of the interval-valued intuitionistic hesitant fuzzy weighted averaging (IVIHFWA), interval-valued intuitionistic hesitant fuzzy weighted geometric (IVIHFWG), GIVIHFWA, and GIVIHFWG operators obtained by using different choices of the input arguments and the weight vector

Summary

Introduction

In many practical problems, when defining the membership degree of an element, the difficulty of establishing the membership degree is not because we have a margin of error (as in intuitionistic fuzzy sets [1] and interval-valued fuzzy sets [2]) or some possibility distribution (as in type 2 fuzzy sets [3]) on the possibility values, but because we have several possible numerical values To deal with such cases, Torra [4] introduced the concept of hesitant fuzzy set to permit the membership of an element to be a set of several possible values between 0 and 1, which can depict the human’s hesitance more objectively and precisely. The degree to which the alternative satisfies the attribute can be represented by an interval-valued intuitionistic hesitant fuzzy set {([0.5, 0.7], [0.2, 0.3]), ([0.2, 0.3], [0.5, 0.6]), ([0.4, 0.6], [0.1, 0.3])}. In many multiple attribute group decision-making (MAGDM) problems, considering that the estimations of the attribute values are interval-valued intuitionistic hesitant fuzzy sets, it is very necessary to give some aggregation techniques to aggregate the interval-valued intuitionistic hesitant fuzzy information.

Preliminaries

Hesitant Fuzzy Sets and Hesitant Fuzzy Elements

The Application of the Developed Approach in Group Decision-Making Problems

Y1 Y2 Y3 Ranking

Conclusions