A coalitional value for fuzzy games with a coalition structure

In this paper, we shall study another coalitional value for fuzzy games with a coalition structure, which is named the proportional coalitional Shapley value. A generalized form of the proportional coalitional Shapley value for fuzzy games with a coalition structure is considered, which can be regarded as a generalization of crisp case. The axiomatic systems of this value are researched. When the original fuzzy game is fuzzy convex, the relationship between the proportional coalitional Shapley value, the fuzzy quotient core and the fuzzy quotient population monotonic allocation scheme (FQPMAS) is researched.

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