A Linear Interactive Solution Concept for Fuzzy Multiobjective Games

Abstract

In this paper, we deal with multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. The aim of the paper is to explain new concepts of solutions for multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. A degree of attainment of the fuzzy goal is defined and the max-min strategy with respect to the degree of attainment of the fuzzy goal is examined. If all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear, the max-min solution is formulated as a nonlinear programming problem. The problem can be reduced to a linear programming problem by making use of Sakawa's method, the variable transformation by Charnes and Cooper and the relaxation procedure.