Maojun Zhang

A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.

Interval programming models for matrix games with interval payoffs

The aim of this paper is to study how to solve a type of matrix game with interval payoffs. In this paper, the interval inequality relations and the concept of solutions of the matrix game with interval payoffs are defined. Based on the fuzzy ranking index defined, the solution of the matrix game with interval payoffs can be obtained through solving a pair of bi-objective linear programming models derived from the constructed auxiliary interval programming models. It is shown that the models proposed in this paper extend those of the classical matrix game. The validity and applicability of the proposed methodology are illustrated with a numerical example.

A methodology for matrix games with payoffs of triangular intuitionistic fuzzy number

The main objective of this paper is to develop a new ranking methodology for solving matrix games with intuitionistic fuzzy payoffs in terms of a value and ambiguity of triangular intuitionistic fuzzy numbers (TIFNs). In order to obtain an equilibrium solution of this matrix game, we construct two auxiliary TIFN programming models that are transformed into bi-objective linear programming models which are solved by a lexicographic methodology. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example.

The Linear Programming Approach to Matrix Games with Payoffs of Intuitionistic Fuzzy Sets

The aim of this paper is to develop the concept and methodology of matrix games with payoffs of intuitionistic fuzzy sets (IF-sets). The definition of matrix games with payoffs of IF-sets is given and according to the concept of the Pareto solutions, the concept of solutions for the game is defined. It is proven that the solutions of matrix games with payoffs of IF-sets can be obtained through solving a pair of linear programming models. The proposed method is shown to be effective and practical by a numerical example, and can be applied to game problems with intuitionistic fuzzy information.