Shapley Value of a Cooperative Game with Fuzzy Set of Feasible Coalitions
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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.
Keywordsfuzzy set type 2 fuzzy set Shapley value cooperative games
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