The Shapley function for n-person fuzzy cooperative games with combined weighted form

Abstract

In this study, a new characteristic function with combined weighted form is developed to fuzzy cooperative games based on the BUM functions. By establishing efficiency, symmetry and additivity axioms, a Shapley function with combined weighted form is presented for fuzzy cooperative games. The proposed Shapley function considers not only the weighted average value of the marginal contribution, but also the collective cooperation tendency of players. Moreover, some desirable properties are introduced simultaneously. We show that the Shapley function with combined weighted form belong to fuzzy core when the fuzzy cooperative games is strong convex. Finally, a numerical example is provided to illustrate the validity of the proposed Shapley function.