The Shapley Function for Fuzzy Cooperative Games with Interval Payoffs

Fuzzy cooperative games with interval payoffs are discussed by defining subtraction operation for internal numbers. A Shapley function axiomatic system for fuzzy games with interval payoffs is given, which is an extension of the Shapley function axiomatic system for traditional fuzzy games. The existence and uniqueness of the given interval Shapley function are proved. Finally, a numerical example is offered to illustrate the utility of the given interval Shapley function.