Profit allocation scheme among partners in virtual enterprises based on Shapley values with fuzzy payoffs

Virtual enterprises (VE) can be viewed as a cooperative alliance of member companies. An important part of the operation of VE is how to allocate the profit among partners in uncertain environment. This case can be viewed as a fuzzy cooperation game. In this paper, we make a study of the Shapley values with the fuzzy payoff functions from the viewpoint that the payoffs of each coalition are often only imprecisely or ambiguously known to the players. Axioms of the classical Shapley value are extended to the fuzzy Shapley values. From the viewpoint that the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, we proposed a crisp allocation scheme based on fuzzy Shapley values.