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The consistent value for fuzzy games: alternative axiomatizations

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Abstract

In the framework of fuzzy transferable-utility games, we propose alternative reduced games by considering the players and their activity levels simultaneously. Further, we characterize the consistent value by means of related consistency and different properties.

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Notes

  1. A cooperative game with fuzzy coalitions was introduced by Aubin (1974, 1981), Butnariu (1978).

References

  • Aubin, J. P. (1974). Coeur et valeur des jeux flous à paiements latèraux. Comptes Rendus de l’Académie des Sciences, 279, 891–894.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Branzei, R., Dimitrov, D., & Tijs, S. (2003). Convex fuzzy games and participation monotonic allocation schemes. Fuzzy Sets and Systems, 139, 267–281.

    Article  MathSciNet  MATH  Google Scholar 

  • Branzei, R., Dimitrov, D., & Tijs, S. (2004). Egalitarianism in convex fuzzy games. Mathematical Social Sciences, 47, 313–325.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Butnariu, D. (1980). Stability and Shapley value for an \(n\)-persons fuzzy game. Fuzzy Sets and Systems, 4, 63–72.

    Article  MathSciNet  MATH  Google Scholar 

  • Butnariu, D., & Klement, T. (1993). Triangular norm-based measures and games with fuzzy coalitions. Dordrecht: Kluwer Academic Publishers.

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Hart, S., & Mas-Colell, A. (1989). Potential, value and consistency. Econometrica, 57, 589–614.

    Article  MathSciNet  MATH  Google Scholar 

  • Hwang, Y. A., & Liao, Y. H. (2009). The consistent value of fuzzy games. Fuzzy Sets and Systems, 160, 644–656.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Liao, Y. H. (2013). The equal allocation of nonseparable costs: An extension under fuzzy behavior. Fuzzy Sets and Systems, 231, 84–94.

    Article  MathSciNet  MATH  Google Scholar 

  • Maschler, M., & Owen, G. (1989). The consistent Shapley value for hyperplane games. International Journal of Game Theory, 18, 389–407.

    Article  MathSciNet  MATH  Google Scholar 

  • Shapley, L. S. (1953). A value for n-person game. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the theory of games II. Annals of mathematics studies (Vol. 28, pp. 307–317). Princeton: Princeton University Press.

  • Tsurumi, M., Tanino, T., & Inuiguchi, M. (2001). A Shapley function on a class of cooperative fuzzy games. Eupopean Journal of Operational Research, 129, 596–618.

    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 

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Authors and Affiliations

  1. Department of Applied Mathematics, National Pingtung University, Pingtung, 900, Taiwan

    Yu-Hsien Liao

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  1. Yu-Hsien Liao
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Correspondence to Yu-Hsien Liao.

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The author is grateful to the editor, the associate editor and the anonymous referee for very helpful suggestions and comments.

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Liao, YH. The consistent value for fuzzy games: alternative axiomatizations. Fuzzy Optim Decis Making 15, 129–138 (2016). https://doi.org/10.1007/s10700-015-9218-4

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  • DOI: https://doi.org/10.1007/s10700-015-9218-4

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