Profit Allocation in Production Cooperative Game Based on Interval Shapley Value

Profit allocation in uncertain product cooperative game is studied. Axioms of Shapley value as given by Shapley are extended to the interval Shapley value. The explicit and exclusive interval Shapley values are put forward. A new interval Shapley value has been proposed. The profit allocation scheme based on interval Shapley value is the interval range including all the real imputation by any possibility. Because the interval number is a special kind of fuzzy numbers, the results of this paper lays a foundation for the research on solutions of cooperative games in other fuzzy forms of payoffs.