Hesitant fuzzy dual Muirhead mean operators and its application to multiple attribute decision making

The present work is focused on hesitant fuzzy multi-attribute decision making (HF-MADM) problem with the hesitant fuzzy information based on a new aggregation operator. To begin with, we present the new hesitant fuzzy dual Muirhead mean (HFDMM) to deal with MADM problems, including the HFDMM and the hesitant fuzzy dual weighted Muirhead mean (HFDWMM) operator, the main advantages of the two 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. In addition, some properties of HFDMM and HFDWMM 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 based on HFDWMM. 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 proposed methods by comparing with the other existing methods are also analyzed by the example.