Mehar approach for solving matrix games with triangular dual hesitant fuzzy payoffs

The dual hesitant fuzzy set (DHFS) is an effective mathematical approach to deal with the data which are imprecise, uncertain or incomplete information. DHFS is an extension of hesitant fuzzy sets (HFS) which encompass fuzzy sets (FS), intuitionistic fuzzy sets (IFS), HFS, and fuzzy multisets as a special case. DHFS consist of two parts, that is, the membership and non-membership degrees which are represented by two sets of possible values. Therefore, in accordance with the practical demand these sets are more flexible and provide much more information about the situation. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of triangular dual hesitant fuzzy numbers (TDHFNs). The flaws of the existing approach to solve matrix games with TDHFNs payoffs are pointed out. Moreover, to resolve these flaws, novel, general and corrected approach called Mehar approach is proposed to obtain the optimal strategies for TDHFNs matrix games. In this methodology, the concepts and ranking order relations of TDHFNs are defined. A pair of bi-objective linear programming models for matrix games with payoffs of TDHFNs is derived from two auxiliary dual hesitant fuzzy programming models based on the ranking order relations of TDHFNs defined in this paper. An effective methodology based on the weighted average method is developed to determine optimal strategies for two players. In this approach, it is verified that any matrix game with TDHFNs payoffs always has a TDHFNs equilibrium value. Finally, a numerical experiment is incorporated to illustrate the applicability and feasibility of the proposed Mehar approach in TDHFNs matrix game. The obtained results are compared with the results obtained by the previous approaches for solving TDHFNs matrix game.