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The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

Author

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  • Jinhui Pang
  • Xiang Chen
  • Shujin Li

Abstract

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

Suggested Citation

  • Jinhui Pang & Xiang Chen & Shujin Li, 2014. "The Shapley Values on Fuzzy Coalition Games with Concave Integral Form," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, January.
    • Handle: RePEc:hin:jnljam:231508
    DOI: 10.1155/2014/231508
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