The Shapley Value on a Kind of Cooperative Fuzzy Games

In this paper, we introduce and investigate a new type of cooperative fuzzy games, which is called cooperative fuzzy games with multilinear form. As will be seen, this kind of fuzzy games is both continuous and monotone nondecreasing with regard to the players' participation rates. The specific expression of the Shapley function for this class of fuzzy games is given, and its existence and uniqueness are discussed. Meantime, an equivalent form of the fuzzy core of the given fuzzy games is studied. Furthermore, the relationship between the Shapley function, the fuzzy core and the fuzzy population monotonic allocation scheme (FPMAS) are discussed. Finally, an example is given.

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