Coalitional game with fuzzy payoffs and credibilistic core

As an important branch of game theory, coalitional game deals with situations that involve cooperation among the players. This paper deals with this topic further by incorporating the fuzzy payoff information. Based on the credibility theory, we introduce two decision criteria to define the preferences of players, which leads to two definitions of credibilistic cores-the solution of coalitional game with fuzzy transferable payoffs. Meanwhile, we give a sufficient and necessary condition to ensure non-emptiness of the credibilistic cores. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.