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The Interaction Among Players in Fuzzy Games

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Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

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Abstract

In this paper, the derivative among levels is defined which characterize the interaction among participation levels in fuzzy coalition. At the same time, the concept of independence among levels based on a coalition is established. Based on these concepts and the assumption that fuzzy characteristic functions concerned are continuous, the (absolute) interaction among levels with respect to other players is defined, then the (absolute) interaction among players with respect to other players is defined and the properties of absolute interaction among players are proved as well.

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References

  1. Owen, G.: Multilinear extensions of games, Management Sci., 1864-1879 (1971/72)

    Google Scholar 

  2. Murofushi, T., Soneda, S.: Techniques for reading fuzzy measures (iii): interaction index. In: Nineth Fuzzy System Symposium, Saporo, Japan, pp. 693–696 (1993)

    Google Scholar 

  3. Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92(2), 167–189 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grabisch, M., Roubens, M.: An axiomatic approach to the concept of interaction among players in cooperative games. Int. J. Game Theory 28, 547–565 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kojadinovic, I.: Modeling interaction phenomena using fuzzy measures: on the notions of interaction and independence. Fuzzy Sets and Systems 135(3), 317–340 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kojadinovic, I.: An axiomatic approach to the measurement of the amount of interaction among criteria or players. Fuzzy Sets and Systems 152(3), 417–435 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    Google Scholar 

  8. Grabisch, M.: The interaction and Mobius representations of fuzzy measures on finite spaces, k-additive measures: a survey. In: Grabisch, M., Murofushi, T., Sugeno, M. (eds.) Fuzzy Measures and Integrals-Theory and Applications, pp. 70–93. Physica Verlag, Heidelberg (2000)

    Google Scholar 

  9. Aubin, J.P.: Mathematical Methods of Game and Economic Theory. North-Holland, Amsterdam (1979)

    MATH  Google Scholar 

  10. Aubin, J.P.: Cooperative fuzzy game: the static and dynamic points of view. TIMS/Studies in the Management Science 20, 407–428 (1984)

    MathSciNet  Google Scholar 

  11. Butnaviu, D.: Fuzzy games; a description of the concept. Fuzzy Sets and Systems 1, 181–192 (1978)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Bing-Yuan Cao

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© 2007 Springer-Verlag Berlin Heidelberg

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Li, Sj., Zhang, Q. (2007). The Interaction Among Players in Fuzzy Games. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_62

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  • DOI: https://doi.org/10.1007/978-3-540-71441-5_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

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