The Fuzzy ESL Values for a Class of Cooperative Games with Fuzzy Payoffs

In a cooperative game with fuzzy payoff value (i.e., fuzzy TU- game), the fuzzy Shapley value is the fuzzy expected value of player marginal contribution, which is also an extension of Shapley value. As the ESL value (satisfying efficiency, symmetry and linearity) is a generalized form of Shapley value for a cooperative game, the relative marginal contribution of player is taken into consideration. Following the ESL value, interaction between coalitions in a fuzzy TU-game is also need to consider. In this study, we extend the fuzzy Shapley value based on the fuzzy payoff value and propose the fuzzy ESL value (i.e., F-ESL value) for a class of fuzzy TU-games. As a generalized form of potential function, a weighted fuzzy potential function to introduced to characterize the F-ESL value. This F-ESL value has a certain degree of flexibility by considering the interaction between coalitions. The proposed fuzzy ESL value is generalized value for a class of fuzzy TU-games, including the Shapley value, the ESL value, and the fuzzy Shapley value, which has a wider range of applications.