Note on distance measure of hesitant fuzzy sets

Distance measure is an important tool for distinguishing the difference between two objects. To study the applications of hesitant fuzzy sets, several distance measures between hesitant fuzzy sets have been proposed. In this paper, we point out some drawbacks of the existing distance measures by counterexamples. Furthermore, we introduce the concept of hesitance degree of hesitant fuzzy element to describe the decision maker’s hesitance in decision making process, and present some new distance measures between hesitant fuzzy sets which contain the hesitance degrees of hesitant fuzzy elements to overcome such drawbacks. Finally, a numerical example is provided to compare the proposed distance measures with the existing distance measures. The results illustrate the validity and applicability of our proposed distance measures.