The Shapley value for fuzzy games on vague sets
نویسندگان
چکیده
In this paper, a general expression of the Shapley value for fuzzy games on vague sets is proposed, where the player participation levels are vague sets. The existence and uniqueness of the given Shapley value are showed by establishing axiomatic system. When the fuzzy games on vague sets are convex, the given Shapley value is a vague population monotonic allocation function (VPMAF) and an element in the core. Furthermore, we study a special kind of this class of fuzzy games, which can be seen as an extension of fuzzy games with multilinear extension form. An application of the proposed model in joint production problem is provided. Key-Words: fuzzy game; vague set; Shapley value; core; multilinear extension
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