Fuzzy cooperative game with intersecting priori coalition: A generalized configuration value

Abstract

A fuzzy game with a configuration structure (i.e., a fuzzy configuration structure game) is introduced, which not only allows the fuzzy participation of players but also admits the intersection of fuzzy priori coalitions. A kind of fuzzy configuration structure games is proposed by the linear expression of cooperative game. In order to seek appropriate solutions for the proposed fuzzy configuration structure game, we prove that the fuzzy value for a fuzzy configuration structure game (i.e., FC value) can be denoted by value of cooperative game by different ways (or formulas). This kind of FC values contains several kinds of values, which is a generalized value of fuzzy cooperative games. Moreover, a further generalized extension of the proposed FC value is also given, which is also seen as an extension of ESL value (satisfying the efficiency, linearity and symmetry). Thus, by fuzzy configuration structure game and its generalized value, the application scope of the cooperative game with a configuration structure is extended to the fuzzy field. A general profit allocation rule is gotten for most kinds of cooperative games, including cooperative game, coalition structure game, configuration structure game and their fuzzy forms.