Multiobjective Bimatrix Game with Fuzzy Payoffs and Its Solution Method using Necessity Measure and Weighted Tchebycheff Norm

In this paper, we propose an interactive algorithm for multiobjective bimatrix games with fuzzy payoffs. Using necessity measure and the weighted Tchebycheff norm method, an equilibrium solution concept is defined, which depends on weighting vectors specified by each player. Since it is very difficult to obtain such equilibrium solutions directly, instead of equilibrium conditions in the necessity measure space, equilibrium conditions in the expected payoff space are provided. Under the assumption that a player can estimate the opponent player’s preference as the weighting vector of the weighted Tchebycheff norm method, the interactive algorithm is proposed to obtain a satisfactory solution of the player from among an equilibrium solution set by updating the weighting vector.