Weighted dual hesitant fuzzy set and its application in group decision making

Abstract

Abstract The dual hesitant fuzzy set(DHFS) is a useful tool to deal with situations in which people are hesitant about providing their satisfaction degree and dissatisfaction degree. In this paper, we introduce the concepts of weighted dual hesitant fuzzy set(WDHFS) and weighted dual hesitant fuzzy element(WDHFE). Furthermore, we introduce some basic operations such as union, intersection, complement, multiplication and power operation of weighted dual hesitant fuzzy elements, investigate their operation properties, propose the score function and the accuracy function of WDHFE to compare two weighted dual hesitant fuzzy elements, and present two kinds of aggregation operators such as WDHFWA operator and WDHFWG operator to fuse weighted dual hesitant fuzzy information. Besides, we introduce the concept of hesitance degree of WDHFE, and propose a distance measure between weighted dual hesitant fuzzy elements based on the feature vector of WDHFE, which satisfies the four properties including triangle inequality. In addition, we develop an approach to group decision making based on the weighted dual hesitant fuzzy environment. Finally, two numerical examples are used to illustrate the effectiveness and practicality of our proposed approach.