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Fuzzy Sets and Systems
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Fuzzy Sets and Systems: Theory and Applications
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Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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Fuzzy and Multiobjective Games for Conflict Resolution (Studies in Fuzziness and Soft Computing)
Studying interval valued matrix games with fuzzy logic
Soft Computing - A Fusion of Foundations, Methodologies and Applications
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Robotics and Computer-Integrated Manufacturing
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Solving mathematical programs with fuzzy equilibrium constraints
Computers & Mathematics with Applications
Soft matrix theory and its decision making
Computers & Mathematics with Applications
Solutions for fuzzy matrix games
Computers & Mathematics with Applications
Application of level soft sets in decision making based on interval-valued fuzzy soft sets
Computers & Mathematics with Applications
IEEE Transactions on Fuzzy Systems
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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Constrained matrix games with payoffs of triangular fuzzy numbers (TFNs) are a type of matrix games with payoffs expressed by TFNs and sets of players' strategies which are constrained. So far as we know, no study have yet been attempted for constrained matrix games with payoffs of TFNs since there is no effective way to simultaneously incorporate the payoffs' fuzziness and strategies' constraints into classical and/or fuzzy matrix game methods. The aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of TFNs. In this methodology, we introduce the concepts of Alpha-constrained matrix games for constrained matrix games with payoffs of TFNs and the values. By the duality theorem of linear programming, it is proven that players' gain-floor and loss-ceiling always have a common interval-type value and hereby any Alpha-constrained matrix game has an interval-type value. Moreover, using the representation theorem for the fuzzy set, it is proven that any constrained matrix game with payoffs of TFNs always has a TFN-type fuzzy value. The auxiliary linear programming models are derived to compute the lower and upper bounds of the interval-type value and optimal strategies of players for any Alpha-constrained matrix game. In particular, the mean and the lower and upper limits of the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs can be directly obtained through solving the derived three linear programming models with data taken from only 1-cut and 0-cut of payoffs. Hereby the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs are easily computed. The proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example.