This study investigates supply chain contracts with a supplier and multiple competing retailers in a fuzzy demand environment. The market demand is considered as a positive triangular fuzzy number. The models of centralized decision, return contract, and revenue-sharing contract are built by the method of fuzzy cut sets theory, and their optimal policies are also proposed. Finally, an example is given to illustrate and validate the models and conclusions. It is shown that the optimal total order quantity of the retailers fluctuates at the center of the fuzzy demand. With the rise of the number of retailers, the optimal order quantity and the fuzzy expected profit for each retailer will decrease, and the fuzzy expected profit for supplier will increase.
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