Games With Fuzzy Payment Matrix
DOI:
https://doi.org/10.21638/11701/spbu31.2020.06Abstract
We consider a method for solving an antagonistic game with a fuzzy payment matrix based on converting fuzzy estimates of the consequences of possible strategies into an integral estimate in the form of an equivalent fuzzy set with a triangular membership function. The method does not impose restrictions on the type of membership functions for fuzzy elements of the payment.
Keywords:
fuzzy set, fuzzy number, membership function, fuzzy payment matrix
Downloads
Download data is not yet available.
References
Bector, C. R. and S. Chandra (2010). Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer
Campos, L. (1989). Fuzzy linear programming model to solve fuzzy matrix games. Fuzzy Sets and Systems, 32(3), 275–289
Cevikel, A. C. and M. Ahlatcloglu (2010). Solution for fuzzy matrix games. Computer and Mathematics with Applications, 60, 399–410
Chaker, A., A. C. Dariani and C. Lucas (2008). How can fuzzy logic determine game equilibriums better. Intelligent Systems (IS'08), 4-th International IEEE Conference, 1, 2-51–2-56
Chang, P.-T. (1994). Ranking of Fuzzy Sets Based on the Concept of Existence. Computers and mathematics with applications, 27, 1–21
Chernov, V. G., I. A. Andreev, D. A. Gradusov and D. V. Tretyakov (1998). The solution of business problems by means of fuzzy algebra. Torah-Center: Moscow (in Russian)
Chernov, V. G. (2018). Comparison of fuzzy numbers based on the construction of a linear relationship of order. Dynamics of complex systems - XXI century, 2, 81–87 (in Russian)
Dubois, D. and H. Prade (1980). Theorie des Possibilites. Applications a la representation des conisisancesen in for natique. Masson
Dutta, B. and S. Gupta (2006). On Nash equilibrium strategy of two-person zero-sum games with trapezoidal fuzzy payoffs. Fuzzy Information and Engineering, 6(3), 299–314
Falomkina, O. V. (2009). Statistical fuzzy games. MGU: Moscow. (in Russian)
Higast, M. and G. J. Klir (1983). Measures of uncertainty and information based of possibility distribution. Int. J. General Systems, 9(1), 43–58
Orlovsky, S. A. (1976). Games in a fuzzy environment. Journal of Computational Mathematics and Mathematical Physics, 6(16), 1427–1435 (in Russian)
Piegat, A. (2013). Fuzzy modeling and control. Physica: Verlog
Qiu, D. Y. Xing and S. Chen (2018). Solving fuzzy matrix games through a ranking value function method. J. Math. Computer Sci., 18, 175–183
Rao, P. P. B. and N. R. Shankar (2012). Ranking generalized fuzzy numbers using area, mode, spread and weight. International Journal of Applied Science and Engineering, 10(1), 41–57
Sahoo, L. (2015). Effect of defuzzification methods in solving fuzzy matrix games. Journal of New Theory, 8, 51–64
Sahoo, L. (2017). An approach for solving fuzzy matrix games using signed distance method. UK Journal of Information and Computing Science, 12(1), 73–80
Seagal, A. V. (2011). Game-theoretic model of investment decision making. Scientific notes of the Taurida National University named after V. I. Vernadsky, a series of "Economics and Management", 1(63), 193–205
Seikh, M. R. , P. K. Nayak, and M. Pal (2015). An alternative approach for solving fuzzy matrix games. International Journal of Mathematics and Soft Computing, 5(1), 79–92
Seraya, O. V. and T. N. Katkova (2012). The task of the theory of games with a fuzzy payment matrix. Mathematical Machines and Systems, 3, 29–36
Stalin, T. and M. Thirucheran (2015). Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic Fuzzy Numbers. International Journal for Scientific Research and Development, 3(10), 1006–1010
Vasilevich, L. F. (2010). Solution of fuzzy matrix games. zavantag.com /docs/2010/index21314.html
Ventzel, E. S. (2004). Operations research. Tasks, principles, methodology. Drofa: Moskow (in Russian)
Vovk, S. P. (2012). A game of two persons with fuzzy strategies and preferences. Almanac of modern science and education, 7(85), 479–485 (in Russian)
Yager, R. R. (1977). Multi-objective decision-making using a fuzzy sets. Intern. J. Man-Machine Studies, 9(4), 375–382
Zaichenko, Yu. P. (2010). Game models of decision making in conditions of uncertainty. In: Proceedings of the V international seminar school "Theory of decision-making". Uzhgorod (in Ukrainian)
Downloads
Published
2022-02-02
How to Cite
Chernov, V. G. (2022). Games With Fuzzy Payment Matrix. Contributions to Game Theory and Management, 13. https://doi.org/10.21638/11701/spbu31.2020.06
Issue
Section
Articles
License
Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
