Skip to main content
SpringerLink
Log in

Unifying the proper cores and dominance cores of cooperative fuzzy games

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

The purpose of this paper is to investigate the equalities of different types of proper cores and dominance cores for the general worth function \(v\) without assuming it to be nonnegative. The different sufficient conditions are provided in this paper to guarantee the equalities of different proper cores and dominance cores for this general situation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aubin, J.-P. (1981). Locally lipschitz cooperative games. Journal of Mathematical Economics, 8, 241–262.

    Article  MathSciNet  MATH  Google Scholar 

  • Aubin, J.-P. (1981). Cooperative fuzzy games. Mathematics of Operations Research, 6, 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  • Azrieli, Y., & Lehrer, E. (2007). On some families of cooperative fuzzy games. International Journal of Game Theory, 36, 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Bector, C. R., Chandra, S., & Vijay, V. (2004). Matrix games with fuzzy goals and fuzzy linear programming duality. Fuzzy Optimization and Decision Making, 3, 255–269.

    Article  MathSciNet  MATH  Google Scholar 

  • Borkotokey, S. (2008). Cooperative games with fuzzy coalitions and fuzzy characteristic functions. Fuzzy Sets and Systems, 159, 138–151.

    Article  MathSciNet  MATH  Google Scholar 

  • Butnariu, D. (1978). Fuzzy game: A description of concept. Fuzzy Sets and Systems, 1, 181–192.

    Article  MathSciNet  MATH  Google Scholar 

  • Butnariu, D., & Kroupa, T. (2008). Shapley mappings and the cumulative value for \(n\)-person games with fuzzy coalitions. European Journal of Operational Research, 186, 288–299.

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, S.-S., & Tan, K.-K. (2002). Equilibria and maximal elements of abstract fuzzy economies and qualitative fuzzy games. Fuzzy Sets and Systems, 125, 389–399.

    Article  MathSciNet  MATH  Google Scholar 

  • Espin, R., Fernendez, E., Mazcorro, G., & Lecich, M. I. (2007). A fuzzy approach to cooperative n-person games. European Journal of Operational Research, 176, 1735–1751.

    Article  MathSciNet  MATH  Google Scholar 

  • Garagic, D., & Cruz, J. B. (2003). An approach to fuzzy noncooperative nash games. Journal of Optimization Theory and Applications, 118, 475–491.

    Article  MathSciNet  MATH  Google Scholar 

  • Guiasu, S. (2000). Coping with uncertainty in \(n\)-person games. International Journal of Uncertaint, Fuzziness and Knowledge-Based Systems, 8, 503–523.

    Article  MathSciNet  MATH  Google Scholar 

  • Hwang, Y.-A., & Liao, Y.-H. (2008). Max-consistency complement-consistency and the core of fuzzy games. Fuzzy Sets and Systems, 159, 152–163.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, S., & Zhang, Q. (2008). The measure of interaction among players in games with fuzzy coalitions. Fuzzy Sets and Systems, 159, 119–137.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, S., & Zhang, Q. (2009). A simplified expression of the shapley function for fuzzy game. European Journal of Operational Research, 196, 234–245.

    Article  MathSciNet  MATH  Google Scholar 

  • Maeda, T. (2003). On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs. Fuzzy Sets and Systems, 139, 283–296.

    Article  MathSciNet  MATH  Google Scholar 

  • Mareš, M. (2000). Fuzzy coalition structures. Fuzzy Sets and Systems, 114, 23–33.

    Article  MATH  Google Scholar 

  • Mareš, M., & Vlach, M. (2001). Linear coalitional games and their fuzzy extensions. International Journal of Uncertaint, Fuzziness and Knowledge-Based Systems, 9, 341–354.

    Article  MATH  Google Scholar 

  • Molina, E., & Tejada, J. (2002). The equalizer and the lexicographical solutions for cooperative fuzzy games: Characterization and properties. Fuzzy Sets and Systems, 125, 369–387.

    Article  MathSciNet  MATH  Google Scholar 

  • Tijs, S. H., Branzei, M. R., Ishihara, S., & Muto, S. (2004). On cores and stable sets for fuzzy games. Fuzzy Sets and Systems, 146, 285–296.

    Article  MathSciNet  MATH  Google Scholar 

  • Vidyottama, V., Chandra, S., & Bector, C. R. (2004). Bi-matrix games with fuzzy goals and fuzzy pay-offs. Fuzzy Optimization and Decision Making, 3, 327–344.

    Article  MathSciNet  MATH  Google Scholar 

  • Vijay, V., Chandra, S., & Bector, C. R. (2005). Matrix games with fuzzy goals and fuzzy payoffs. Omega, 33, 425–429.

    Article  Google Scholar 

  • Vijay, V., Mehra, A. V., Chandra, S., & Bector, C. R. (2007). Fuzzy matrix games via a fuzzy relation approach. Fuzzy Optimization and Decision Making, 6, 299–314.

    Article  MathSciNet  MATH  Google Scholar 

  • Wu, H.-C. (2012). Proper cores and dominance cores of fuzzy games. Fuzzy Optimization and Decision Making, 11, 47–72.

    Article  MathSciNet  MATH  Google Scholar 

  • Wu, H.-C. (2012). Cores of fuzzy games and their convexity. Fuzzy Sets and Systems, 198, 59–69.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

Authors
  1. Hsien-Chung Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hsien-Chung Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, HC. Unifying the proper cores and dominance cores of cooperative fuzzy games. Fuzzy Optim Decis Making 14, 243–263 (2015). https://doi.org/10.1007/s10700-014-9203-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-014-9203-3

Keywords

Search

Navigation