Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making

Fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set can be regarded as a special case of dual hesitant fuzzy set. Therefore, dual hesitant fuzzy set is a more comprehensive set. Further, Archimedeant-norm andt-conorm provides generalized operational rules for dual hesitant fuzzy set. And geometric Heronian mean have advantages when considering the interrelationship of aggregation arguments. Thus, it is necessary to extend the geometric Heronian mean operator to the dual hesitant fuzzy environment based on Archimedeant-norm andt-conorm. Comprehensive above, in this paper, the dual hesitant fuzzy geometric Heronian mean operator and dual hesitant fuzzy geometric weighted Heronian mean operator based on Archimedeant-norm andt-conorm are developed. Their properties and special case are investigated. Moreover, a multiple attribute decision making method is proposed. The effectiveness of our method and the influence of parameters on multiple attribute decision making are studied by an example. The superiority of our method is illustrated by comparing with other existing methods.