Credibility-based cooperative fuzzy game with Choquet integral form

In this paper, we advance an argument on the fuzzy game which was introduced by Tsurumi and Tanino. Fuzzy coalition can be considered as the rates of players' participation to the coalition. We define the participation rates as fuzzy variables to denote the available vagueness information. First, a new concept of payoff function was given from the Choquet integral fuzzy measure point of view, and a new type of fuzzy game was provided to extend the fuzzy game definition. Second, when the players want to maximize the optimistic return at a predetermined confidence level, the payoff function was discussed in detail by credibility measure. Third, a credibility maximization model was developed to meet the different optimistic levels. Finally, we give a numerical example to show the rational property of obtained payoff for fuzzy coalition.