Advertisement

Fuzzy Game Based on Fuzzy Comparison Operator

  • Cunlin Li
  • Lin Zhang
  • Zhifu Jia
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)

Abstract

A fuzzy comparison operator was proposed to explore the fuzzy game. By comparing the fuzzy income of different strategy, the fuzzy equilibrium strategy was established based on a fuzzy comparison operator. At last the necessary and sufficient condition of the fuzzy equilibrium was discussed.

Keywords

Fuzzy games Extension principle Fuzzy comparison operator 

Notes

Acknowledgments

This paper is supported by the National Natural Science Foundation of China (No. 71561001); the Key Social Science Research Base of State Ethnic Affairs Commission of China-Governance and social management research center of Northwest Ethnic regions (No. MWJD 201612); the Foundation of North Minzu University (GLXY201608).

References

  1. 1.
    Nishizaki, I., & Sakawa, M. (2000). Uilibrium solutions in multi-objective bi-matrix games with fuzzy payoffs and fuzzy goals. Fuzzy Sets and Systems, 111, 99–116.CrossRefGoogle Scholar
  2. 2.
    Nishizaki, I., & Sakawa, M. (2001). Fuzzy and multi-objective games for conflict resolution. New York: Physica-Verlag.CrossRefGoogle Scholar
  3. 3.
    Bector, C. R., & Chandra, S. (2005). Fuzzy mathematical programming and fuzzy matrix games. Berlin: Springer.Google Scholar
  4. 4.
    Bector, C. R., & Chandra, S. (2004). Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs. Fuzzy Sets and Systems, 146, 253–269.CrossRefGoogle Scholar
  5. 5.
    Takashi, M. (2003). On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Fuzzy Sets and Systems, 139, 283–296.CrossRefGoogle Scholar
  6. 6.
    Takashi, M. (2000). Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff. Journal of Mathematical Analysis and Applications, 251, 885–896.CrossRefGoogle Scholar
  7. 7.
    Xiangfeng, Y., & Jinwu, G. (2014). Bayesian equilibria for uncertain bimatrix game with asymmetric information. Journal of Intelligent Manufacturing, 12(1), 65–78.Google Scholar
  8. 8.
    Cunlin, L. (2012). Characterization of the equilibrium strategy of fuzzy bimatrix games based on L-R fuzzy variables. Journal of Applied Mathematics, 2012, 1–15.Google Scholar
  9. 9.
    Zadeh, L. A. (1975). The concept of a linguistic variable and its applications in approximate reasoning. Information Sciences, 8, 199–252.CrossRefGoogle Scholar
  10. 10.
    Sakawa, M., & Yano, H. (1991). Feasibility and Pareto optimality for multi-objective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, 43, 1–15.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Cunlin Li
    • 1
  • Lin Zhang
    • 2
  • Zhifu Jia
    • 2
  1. 1.School of Management, North Minzu UniversityYinchuanChina
  2. 2.College of Mathematics and Information Science, North Minzu UniversityYinchuanChina

Personalised recommendations