Abstract
In this paper, a two-person zero-sum game is considered, in which the payoffs are characterized as fuzzy variables. Based on possibility measure, credibility measure, and fuzzy expected value operator, three types of concept of minimax equilibrium strategies, r-possible minimax equilibrium strategy, r-credible minimax equilibrium strategy, and expected minimax equilibrium strategy, are defined. An iterative algorithm based on fuzzy simulation is designed to find the equilibrium strategies. Finally, a numerical example is provided to illustrate the effectiveness of the algorithm.
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References
Campos, L.: Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets and Systems 32, 275–289 (1989)
Liu, B., Iwamura, K.: Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems 94, 227–237 (1998)
Liu, B., Iwamura, K.: A note on chance constrained programming with fuzzy coefficients. Fuzzy Sets and Systems 100, 229–233 (1998)
Liu, B., Liu, Y.: Expected value of fuzzy variable and fuzzy expected value model. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)
Liu, B.: Toward fuzzy optimization without mathematical ambiguity. Fuzzy Optimization and Decision Making 1, 43–63 (2002)
Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Berlin (2004)
Maeda, T.: Characterization of equilibrium strategy of the bi-matrix game with fuzzy payoff. Journal of Mathematical Analysis and Applications 251, 885–896 (2000)
Maeda, T.: On the characterization of equilibrium strategy of two-person zero-sum game with fuzzy payoffs. Fuzzy Sets and Systems 139, 283–296 (2003)
Nahmias, S.: Fuzzy variables. Fuzzy Sets and Systems 1, 97–110 (1978)
Nishizaki, I., Sakawa, M.: Fuzzy and Multiobjective Games for Conflict Resolution. Physica, Heidelberg (2001)
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Xu, L., Zhao, R., Shu, T. (2005). Three Equilibrium Strategies for Two-Person Zero-Sum Game with Fuzzy Payoffs. In: Wang, L., Jin, Y. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2005. Lecture Notes in Computer Science(), vol 3613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539506_44
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DOI: https://doi.org/10.1007/11539506_44
Publisher Name: Springer, Berlin, Heidelberg
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