Similarity Measure of Hesitant Fuzzy Sets Based on Implication Function and Clustering Analysis

Hesitant fuzzy set (HFS) permits several possible values as the membership degree of an element to a set to express the decision makers' hesitance. Since its appearance, HFS has been extensively applied in multi-attribute decision making, group decision making and evaluation process. Considering that the similarity measure of hesitant fuzzy sets (HFSs) is an important index in intelligent system, and the implication function can describe many subtle differences which is very suitable for dealing with hesitant fuzzy information. In this paper, we merge implication function with HFS to investigate the similarity measure of HFSs, propose some new formulas to calculate the similarity measures of HFSs which are different from the existing similarity measures of HFSs based on the distance measure, and do some comparison analysis. Meanwhile, we introduce the union and intersection operations of HFSs, the hesitant fuzzy similar relation and the hesitant fuzzy equivalent relation, and develop the hesitant fuzzy clustering algorithm. Finally, three numerical examples are used to illustrate the effectiveness and validation of our proposed method.