An interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies and the value of the matrix game with payoffs of TIFNs. Based on the cut sets and ranking order relations between TIFNs, the intuitionistic fuzzy programming models are transformed into linear programming models, which are solved using the existing simplex method. Validity and applicability of the proposed methodology are illustrated with a numerical example of the market share problem.