Fuzzy multiobjective programming methods for fuzzy constrained matrix games with fuzzy numbers
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Matrix Games with Fuzzy Goals and Fuzzy Linear Programming Duality
Fuzzy Optimization and Decision Making
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Studying interval valued matrix games with fuzzy logic
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Short Communication: Matrix games with interval data
Computers and Industrial Engineering
Non cooperative fuzzy games in normal form: A survey
Fuzzy Sets and Systems
Application of linear programming with I-fuzzy sets to matrix games with I-fuzzy goals
Fuzzy Optimization and Decision Making
Statistical convergence of order β for generalized difference sequences of fuzzy numbers
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players' strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players' optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.