Cybernetics and Systems Analysis

, Volume 53, Issue 3, pp 432–440 | Cite as

Shapley Value of a Cooperative Game with Fuzzy Set of Feasible Coalitions

  • S. O. MashchenkoEmail author
  • V. I. Morenets


The paper investigates Shapley value of a cooperative game with fuzzy set of feasible coalitions. It is shown that the set of its values is a type 2 fuzzy set (a fuzzy set whose membership function takes fuzzy values) of special type. Furthermore, the corresponding membership function is given. Elements of the support of this set are defined as particular Shapley values. The authors also propose the procedure of constructing these elements with maximum reliability of their membership and reliability of non-membership, not exceeding a given threshold.


fuzzy set type 2 fuzzy set Shapley value cooperative games 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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