In this paper, the coalitional game with fuzzy payoffs is considered. Based on the credibility theory, two new solution concepts of fuzzy coalitional game are proposed, one of which is the expected nucleolus and the other is the α-optimistic nucleolus. Furthermore, the non-emptiness and uniqueness characterizations of credibilistic nucleolus are proved, and the relationship between credibilistic nucleolus and credibilistic core is presented. Two examples are given to demonstrate the solution process.
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