2016 Volume 28 Issue 4 Pages 756-763
In this paper, we consider multiobjectve two-person zero-sum games with fuzzy payoff matrices. In order to deal with fuzzy payoff matrices, the possibility measure concept for the fuzzy goals of each player is introduced. Under the assumption that each player adopts the most disadvantage strategy for the opponent player, a pessimistic Pareto optimal solution concept is defined for each player. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques, even if the membership functions for not only the fuzzy goals of the player but also elements of the fuzzy payoff matrices are nonlinear. We propose an interactive algorithm based on linear programming techniques to obtain a pessimistic compromise solution from among pessimistic Pareto optimal solutions. A numerical example illustrates the interactive processes under a hypothetical player to show the efficiency of the proposed method.
