Optimal fuzzy coalition structure and solution concepts of a class of fuzzy games

In this paper, we make a study on the optimal fuzzy coalition structure and the corresponding imputation of a class of fuzzy cooperative games which are said to be ‘with Choquet integral form’. Using linear programming, we show that optimal fuzzy coalition structure does exist in this class of fuzzy cooperative games. We introduce the extended game in which the coalition worth is just the optimal value of the corresponding linear programming and proof that the extended game always has a nonempty core which can be used as an allocation method in the optimal fuzzy coalition structure. Besides, we also propose another solution concept: the Shapley value of the extended game.