Linear programming approach to matrix games with intuitionistic fuzzy goals

Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-sets. In this methodology, the concepts of IF-set goals and the solutions of matrix games with IF-set goals are proposed. It is proven that solutions of matrix games with IF-set goals can be obtained through solving the developed auxiliary linear programming models, which are the generalization of matrix games with fuzzy goals. The proposed methodology is illustrated with a numerical example. Furthermore, comparison analysis of the proposed methodology is conducted to show its advantages over matrix games with fuzzy goals.