The Cores for Fuzzy Games Represented by the Concave Integral

We propose a new fuzzy game model by the concave integral by assigning subjective expected values to random variables in the interval [0, 1]. The explicit formulas of characteristic functions which are determined by coalition variables are discussed in detail. After illustrating some properties of the new game, its fuzzy core is defined; this is a generalization of crisp core. Moreover, we give a further discussion on the core for the new games. Some notions and results from classical games are extended to the model. The nonempty fuzzy core is given in terms of the fuzzy convexity. Our results develop some known fuzzy cooperative games.