Weighted Interval-Valued Hesitant Fuzzy Sets and Its Application in Group Decision Making

Abstract

The interval-valued hesitant fuzzy set, which allows decision makers to use several interval numbers to assess a variable, is a useful tool to deal with situations in which people are hesitant in providing their interval-valued assessments. In this paper, we introduce the concept of weighted interval-valued hesitant fuzzy set, in which different weights are designed to these possible membership degrees, and the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. Then we define some basic operations such as union, intersection, complement, multiplication and power operation of weighted interval-valued hesitant fuzzy sets and weighted interval-valued hesitant fuzzy elements, discuss their operation properties, and propose the score function of the weighted interval-valued hesitant fuzzy element to compare two weighted hesitant fuzzy elements. Furthermore, we introduce the concept of hesitance degree of weighted interval-valued hesitant fuzzy element, present four aggregation operators such as the weighted interval-valued hesitant fuzzy-weighted averaging operator, the weighted interval-valued hesitant fuzzy-weighted geometric operator, the generalized weighted interval-valued hesitant fuzzy-weighted averaging operator and the generalized weighted interval-valued hesitant fuzzy-weighted geometric operator to aggregate weighted interval-valued hesitant fuzzy information, and build the mathematical model of multi-criteria group decision making based on the expert weights (known and unknown). Finally, a numerical example is given to illustrate the effectiveness and feasibility of our proposed method.