Fuzzy games: A characterization of the core

In this paper we extend to the cooperative fuzzy games case the reduced game introduced by Davis and Maschler [The kernel of a cooperative game, Naval Res. Logist. Quart. 12 (1965) 223–259]. We shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency. We further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse.