The Shapley function for fuzzy cooperative games with multilinear extension form

In this paper, the definition of the Shapley function for fuzzy cooperative games is given, which is obtained by extending the classical case. The specific expression of the Shapley function for fuzzy cooperative games with multilinear extension form is given, and its existence and uniqueness are discussed. Furthermore, the properties of the Shapley function are researched. Finally, the fuzzy core for this kind of game is defined, and the relationship between the fuzzy core and the Shapley function is shown.