Abstract. The present paper investigates Shapley value of a co-operative game with a fuzzy set of feasible coalitions. It is shown that the set of its values is a type-2 fuzzy set (a fuzzy set whose membership function takes fuzzy values) of special type. Furthermore, the corresponding membership function is given. Elements of the support of this set are defined as particular Shapley values. We also propose the procedure of constructing these elements with maximal reliability of their membership and reliability of non membership, not exceeding a given threshold.

Keywords: fuzzy set, type 2 fuzzy set, Shapley value, co-operative games.