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Integral Representations of Cooperative Game with Fuzzy Coalitions

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  • Jinhui Pang
  • Xiang Chen

Abstract

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

Suggested Citation

  • Jinhui Pang & Xiang Chen, 2014. "Integral Representations of Cooperative Game with Fuzzy Coalitions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:639684
    DOI: 10.1155/2014/639684
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    References listed on IDEAS

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    1. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
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