Hesitant Fuzzy Power Bonferroni Means and Their Application to Multiple Attribute Decision Making

As a useful generalization of fuzzy sets, the hesitant fuzzy set is designed for situations in which it is difficult to determine the membership of an element to a set because of ambiguity between a few different values. In this paper, we define the ith-order polymerization degree function and propose a new ranking method to further compare different hesitant fuzzy sets. In order to obtain much more information in the process of group decision making, we combine the power average operator with the Bonferroni mean in hesitant fuzzy environments and develop the hesitant fuzzy power Bonferroni mean and the hesitant fuzzy power geometric Bonferroni mean. We investigate the desirable properties of these new hesitant fuzzy aggregation operators and discuss some special cases. The new aggregation operators are utilized to present techniques for hesitant fuzzy multiple attribute group decision making. Finally, a numerical example is provided to illustrate the effectiveness of the developed techniques.