Power average-based score function and extension rule of hesitant fuzzy set and the hesitant power average operators.

Hesitant fuzzy set, as an extension of fuzzy set, has absorbed many researchers from various scientific backgrounds to deal with uncertainty. Solving decision-making problems is one of the most important applications of hesitant fuzzy set. To do so, it is needed to rank hesitant fuzzy elements (HFEs) and to define some mathematical operations on them. In this paper, a new method based on the power average operator is firstly suggested to compare the HFEs. Given that different HFEs may have different numbers of elements, new procedures are developed to make them uniform. Then, four kinds of hesitant power average operators, including the hesitant power average operator, the weighted hesitant power average operator, the ordered weighted hesitant power average operator and the hybrid weighted hesitant power average operator, are introduced. Finally, a new approach to solve the multiple attribute decision-making problems is introduced via the proposed operators. Numerical examples are given to illustrate and compare the proposed methods.