Intuitionistic Fuzzy Optimization Technique for Nash Equilibrium Solution of Multi-objective Bi-Matrix Games

摘要

In this paper, we present an application of intuitionistic fuzzy optimization model to a two person multi-objective bi-matrix games (pair of pay-offs matrices) for the Nash equilibrium solution(NES) with mixed strategies. We use linear membership and non-membership function for such computation. We introduce the intuitionistic fuzzy(IF) goal for a choice of a strategy in a pay-off matrix in order to incorporate ambiguity of human judgements and a player wants to maximize his/her degree of attainment of the IF goal. It is shown that this NES is the optimal solution of the mathematical programming problem, namely a quadratic programming problem. In addition, numerical example is also presented to illustrate the methodology.