Hesitant Fuzzy Muirhead Mean Operators And Its Application To Multiple Attribute Decision Making

In this paper, we investigate the multiple attribute decision making (MADM) problems with the hesitant fuzzy information based on a new aggregation operator. To begin with, we present the new hesitant fuzzy Muirhead mean operator to deal with MADM problems with hesitant fuzzy information, including the hesitant fuzzy Muirhead mean (HFMM) operator, the hesitant fuzzy weighted Muirhead mean (HFWMM) operator, the main advantages of these aggregation operators are that they can capture interrelationships of multiple attributes among any number of attributes by a parameter vector P and make information aggregation process more flexible by the parameter vector P, whilst, HFMM and HFWMM are also a generalization of hesitant fuzzy Maclaurin symmetric mean (HFMSM) operator. In addition, some properties of these new aggregation operators are obtained and some special cases are discussed where the parameter vector takes some different values. Moreover, we present a new method to solve the MADM problems with hesitant fuzzy information. Finally, an illustrative example is provided to show the feasibility and validity of the new method, the influences of parameter vector P on the decision making results are investigated and the advantages of the proposed methods by comparing with the other existing methods are also analyzed by the example.