Fuzzy transferable-utility games: a weighted allocation and related results

By considering the supreme-utilities among fuzzy sets and the weights among participants simultaneously, we introduce the supreme-weighted value on fuzzy transferable-utility games. Further, we provide some equivalent relations to characterize the family of all solutions that admit a potential on weights. We also propose the dividend approach to provide alternative viewpoint for the potential approach. Based on these equivalent relations, several axiomatic results are also proposed to present the rationality for the supreme-weighted value.