Axiomatization of Fuzzy Core in Games with Fuzzy Coalition

  • Hong-xia Sun
  • Qiang Zhang
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 78)


In the framework of fuzzy game with fuzzy coalition, an axiomatization of the fuzzy core is provided by using individually rational, consistency, modularity and anti-monotonicity. Further, examples are given to illustrate the independent of the properties which used in the axiomatization of fuzzy core.


Cooperative game coalition structure core consistency weak converse consistency 


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  1. 1.
    Aubin, J.P.: Coeur et valeur des jeux flous à paiements latérau. Comptes Rendus Hebdomadaires des Séances de l’ Académie des Sciences 279-A, 891–894 (1974)MathSciNetGoogle Scholar
  2. 2.
    Aubin, J.P.: Cooperative fuzzy games. Mathematics of Operations Research 6, 1–13 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Branzei, R., Dimitrov, D., Tijs, S.: Convex fuzzy games and participation monotonic allocation schemes. Fuzzy Sets and Systems 139, 267–281 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Branzei, R., Dimitrov, D., Tijs, S.: Egalitarianism in convex fuzzy games. Mathematical Social Sciences 47, 313–325 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Davis, M., Maschler, M.: The kernel of a cooperative game. Naval Research Logistics Quartrely 12, 223–259 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hwang, Y.A., Sudhöter, P.: Axiomatizations of the core on the universal domain and other natural domains. International Journal of Game Theory 29, 597–623 (2001)zbMATHCrossRefGoogle Scholar
  7. 7.
    Hwang, Y.A.: Fuzzy games: A characterization of the core. Fuzzy Sets and Systems 158, 2480–2493 (2007)zbMATHCrossRefGoogle Scholar
  8. 8.
    Hwang, Y.A., Liao, Y.H.: Max-consistency, complement-consistency and the core of fuzzy games. Fuzzy Sets and Systems 159, 152–163 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Keiding, H.: An axiomatization of the core of a cooperative game. Economics Letters 20, 111–115 (1986)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Lerena, F.: An axiomatization of the core of games with restricted cooperation. Economics Letters 95, 80–84 (2007)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Li, S.J., Zhang, Q.: A simplified expression of the Shapley function for fuzzy game. European Journal of Operational Research 196, 234–245 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Moulin, H.: The separability axiom and equal-sharing methods. Journal of Economic Theory 36, 120–148 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Peleg, B.: On the reduced game property and its converse. International Journal of Game Theory 15, 187–200 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Pulido, M.A., Sánchez-Soriano, J.: On the core, the Weber set and Convexity in games with a priori unions. European Journal of Operational Research 193, 457–468 (2009)CrossRefGoogle Scholar
  15. 15.
    Tsurumi, M., Tanino, T., Inuiguchi, M.: A Shapley function on a class of cooperative fuzzy games. European Journal of Operational Research 129, 596–618 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Voorneveld, M., Nouweland, A.: A new axiomatization of the core of games with transferable utility. Economics Letters 60, 151–155 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Yu, X.H., Zhang, Q.: The fuzzy core in games with fuzzy coalitions. Journal of Computational and Applied Mathematics 230, 173–186 (2009)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hong-xia Sun
    • 1
  • Qiang Zhang
    • 1
  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina

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