Solving fuzzy matrix games through a ranking value function method
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Authors
Dong Qiu
- College of Science, Chongqing University of Post and Telecommunication, Chongqing, 400065, P. R. China
Yumei Xing
- College of Science, Chongqing University of Post and Telecommunication, Chongqing, 400065, P. R. China
Shuqiao Chen
- College of Science, Chongqing University of Post and Telecommunication, Chongqing, 400065, P. R. China
Abstract
The objective of this paper is to establish the
bi-matrix games with crisp payoffs based on ranking value function method. We obtain that the equilibrium solution of the game model can be translated into the optimal solution of the non-linear programming problem. Finally, to illustrate the effectiveness and correctness of the obtained model, an example is provided.
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ISRP Style
Dong Qiu, Yumei Xing, Shuqiao Chen, Solving fuzzy matrix games through a ranking value function method, Journal of Mathematics and Computer Science, 18 (2018), no. 2, 175--183
AMA Style
Qiu Dong, Xing Yumei, Chen Shuqiao, Solving fuzzy matrix games through a ranking value function method. J Math Comput SCI-JM. (2018); 18(2):175--183
Chicago/Turabian Style
Qiu, Dong, Xing, Yumei, Chen, Shuqiao. "Solving fuzzy matrix games through a ranking value function method." Journal of Mathematics and Computer Science, 18, no. 2 (2018): 175--183
Keywords
- Fuzzy bi-matrix game
- equilibrium solution
- non-linear programming problem
MSC
References
-
[1]
T. Başar, G. J. Olsder, Dynamic Noncooperative Game Theory, Academic press, London (1995)
-
[2]
C. R. Bector, S. Chandra, Fuzzy mathematical programming and fuzzy matrix games, Springer, Germany (2005)
-
[3]
D. Blackwell, An analog of the minimax theorem for vector payoff, Pacific J. Math., 6 (1956), 1–8.
-
[4]
Y. Chalco-Canoa, A. Rufián-Lizana, H. Román-Flores, R. Osuna-Gómez, A note on generalized convexity for fuzzy mappings through a linear ordering, Fuzzy Sets and Systems, 231 (2013), 70–83
-
[5]
C. B. Das, S. K. Roy, Fuzzy based GA to multi-objective entropy bimatrix game, Opsearch, 50 (2013), 125–140.
-
[6]
A. DeLuca, S. Termini, A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Information and Control, 20 (1972), 301–312.
-
[7]
P. Diamond, P. Kloeden , Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35 (1990), 241–249.
-
[8]
D. J. Dubois, H. Prade, Fuzzy sets and systems-theory and application, Academic Press, New York (1980)
-
[9]
W. Fei, D.-F. Li, Bilinear Programming Approach to Solve Interval Bimatrix Games in Tourism Planning Management, Int. J. Fuzzy Syst., 18 (2016), 504–510.
-
[10]
M. Hladík, Interval valued bimatrix games, Kybernetika, 46 (2010), 435–446.
-
[11]
M. Larbani, Solving bi-matrix games with fuzzy payoffs by introducing nature as a third player, Fuzzy Sets and Systems, 160 (2009), 657–666.
-
[12]
C.-L. Li, Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on Fuzzy Variables, J. Appl. Math., 2012 (2012 ), 15 pages.
-
[13]
D.-F. Li, Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Springer-verlag, Heidelberg (2014)
-
[14]
L. Li, S. Liu, J. Zhang, On fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings, Fuzzy Sets and Systems, 280 (2015), 107–132.
-
[15]
T. Maeda, Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff, J. Math. Anal. Appl., 251 (2000), 885–896.
-
[16]
O. L. Mangasarian, H. Stone, Two person non zero sum game and quadratic programming, J. Math. Anal. Appl., 9 (1964), 348–355.
-
[17]
J.-X. Nan, M.-J. Zhang, D.-F. Li, Intuitionistic fuzzy programming models for matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers, Int. J. Fuzzy Syst., 16 (2014), 444–456.
-
[18]
P. K. Nayak, M. Pal, Bimatrix games with intiutionstic fuzzy goals, Iran. J. Fuzzy Syst., 7 (2010), 65–79.
-
[19]
M. Panigrahi, G. Panda, S. Nanda, Convex fuzzy mapping with differentiability and its application in fuzzy optimization, European J. Oper. Res., 185 (2008), 47–62.
-
[20]
S. K. Roy, Fuzzy programming approach to two-person multicriteria bimatrix games, J. Fuzzy Math., 15 (2007), 141–153.
-
[21]
S. K. Roy, M. P. Biswal, R. N. Tiwari, An approach to multi-objective bimatrix games for Nash equilibrium solutions, Ric. Oper., 30 (2001), 56–63.
-
[22]
Y. R. Syau, E. Stanley Lee, Fuzzy Weirstrass theorem and convex fuzzy mappings, Comput. Math. Appl., 51 (2006), 1741–1750.
-
[23]
Y. R. Syau, E. Stanley Lee, Preinvexity and \(\Phi\)-convexity of fuzzy mappings through a linear ordering, Comput. Math. Appl., 51 (2006), 405–418.
-
[24]
V. Vidyottama, S. Chandra, C. R. Bector, Bi-matrix game with fuzzy goals and fuzzy payoffs, Fuzzy Optim. Decis. Mak., 3 (2004), 327–344.
-
[25]
V. Vijay, A. Mehra, S. Chandra, C. R. Bector, Fuzzy matrix games via a fuzzy relation approach, Fuzzy Optim. Decis. Mak., 6 (2007), 299–314
-
[26]
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.
-
[27]
H.-J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45–55.