Abstract
An approach to get the Nash equilibrium solution of fuzzy matrix game is proposed in this paper. At first, the solution of fuzzy coefficient linear programming is given based on the structured element expression of fuzzy number and the structured element weighted order. Then fuzzy coefficient linear programming is transformed into classical linear programming by using the homeomorphism property between fuzzy number space and the family of standard monotone functions in [-1, 1], which simplifies the solving process of fuzzy Nash equilibrium. Finally, an example is presented to compare the method we proposed with other methods, from which a conclusion may be drawn that the method we proposed is of more validity and practicability.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubin, J.: P1 Mathematicalmethods of game and economic theory. North Holland Press, Amsterdam (1980)
Aubin, J.: P1Cooperative fuzzy games. Mathematical Operation Research 6, 1–13 (1981)
Campos, L.: Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets and System 32(3), 275–289 (1989)
Sakawa, M., Nishizaki, I.: Two-person zero-sum games with multiple goals. In: Proceedings of the Tenth International
MareÍM1: Fuzzy coalition forming. In: Proceedings of 7th IFSA World Congress, Prague, pp. 70–73 (1997)
MareÍM1: Fuzzy coalition structures. Fuzzy Sets and Systems 114, 23–33 (2000)
Maeda, T.: Characterization of the equilibrium strategy of the bi-matrix games. Journal of Mathematical Analysis and Applications 251(2), 885–896 (2000)
Kacher, F., Larbani, M.: Existence of equilibrium solution for a non-cooperative game with fuzzy goals and parameters. Fuzzy Sets and Systems 159(2), 164–176 (2008)
Nishizaki, I., Sakawa, M.: Fuzzy and multiobjective game for conflict resolution. Physica-verleg, Heidelberg (2001)
Bector, C.R., Chandra, S., Vidyottama, V.: Matrix games with fuzzy goals and fuzzy linear programming duality. Fuzzy Optimization and Decision Making 3(3), 255–269 (2004)
Vidyottama, V., Chandra, S.: Bi-matrix games with fuzzy goals and fuzzy pay-offs. Fuzzy Optimization and Decision Making 3(3), 327–344 (2004)
Song, H.J., Yi, J., Li, D.Q.: Matrix games with fuzzy payoff and its solution. Journal of Industrial Engineering/Engineering Management 12(2), 30–34 (1998)
Guo, S.Z.: Principle of Mathematical Analysis Based on Structured Element. Northeast University Press, Shenyang (2004)
Guo, S.Z.: Homeomorphic property between fuzzy number space and family of standard bounded monotone function. Advances in Natural Science 14(11), 1318–1321 (2004)
Guo, S.Z.: Comparison and sequencing of fuzzy numbers based on the method of structured element. Systems Engineering–Theory & Practice 29(3), 106–111 (2009)
Guo, S.Z.: Linear representation of fuzzy number and fuzzy-valued function using fuzzy structured element. Joural of Liaoning Technical University 25(3), 475–477 (2006)
Guo, S.Z.: Transformation Group of Monotone Functions with Same Monotonic Formal on [-1, 1] and Operations of Fuzzy Numbers. Fuzzy Systems and Mathematics 19(3), 105–110 (2005)
Maeda, T.: On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Fuzzy Sets and Systems 139(2), 283–296 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, G., Guo, S., Zhang, Q. (2010). Method for Solving the Fuzzy Matrix Game Based on Structured Element. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-14880-4_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14879-8
Online ISBN: 978-3-642-14880-4
eBook Packages: EngineeringEngineering (R0)