Integral representations of cooperative game with fuzzy coalitions

Classical extensions of fuzzy game models are based on various integrals,such as butnariu game and tsurumi game. a new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with concave integral,where players' expected values are on a partial set of coalitions. some representations and properties of some limited models are compared in this paper. the explicit formula of characteristic function determined by coalition variables is given. moreover,a calculation approach of imputations is discussed in detail. the new game could be regarded as a general form of cooperative game. furthermore,the fuzzy game introduced by tsurumi is a special case of the proposed game when game is convex. © 2014 jinhui pang and xiang chen.