An extension of cooperative fuzzy games

In this paper, a generalized form of fuzzy game is proposed that can be seen as an extension of the cooperative fuzzy game. Players in the proposed fuzzy game do not need to know precise information about the payoff value or to form a crisp coalition. Based on the Hukuhara difference, a game with a fuzzy characteristic function is studied, and the explicit form of a Shapley function is shown. Furthermore, we introduce and investigate a new class of fuzzy game with fuzzy coalitions and a fuzzy characteristic function. Based on the Hukuhara difference and the Choquet integral, we give the explicit form of the Shapley value for the new class of fuzzy game. It has been seen that most of the properties of a crisp game hold well in the proposed fuzzy game. A practical application of the proposed model in joint production problem is also provided.