**Novel Parameterized Distance Measures on Hesitant Fuzzy Sets with Credibility Degree and Their Application in Decision-Making**

**Jiaru Li 1, Fangwei Zhang 1,\*, Qiang Li 2, Jing Sun 3,\*, Janney Yee 4, Shuhong Wang 5 and Shujun Xiao 6**


Received: 5 September 2018; Accepted: 16 October 2018; Published: 1 November 2018

**Abstract:** The subject of this study is to explore the role of cardinality of hesitant fuzzy element (HFE) in distance measures on hesitant fuzzy sets (HFSs). Firstly, three parameters, i.e., credibility factor, conservative factor, and a risk factor are introduced, thereafter, a series of novel distance measures on HFSs are proposed using these three parameters. These newly proposed distance measures handle the relationship between the cardinal number and the element values of hesitant fuzzy set well, and are suitable to combine subjective and objective decision-making information. When using these functions, decision makers with different risk preferences are allowed to give different values for these three parameters. In particular, this study transfers the hesitance degree index to a credibility of the values in HFEs, which is consistent with people's intuition. Finally, the practicability of the newly proposed distance measures is verified by two examples.

**Keywords:** hesitant fuzzy sets; hesitant degree; credibility; distance measure; similarity measure
