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This paper examines a research and development (R&D) optimal stopping decision problem without rivalry in a fuzzy environment. In classical stochastic R&D decision models, the inter-arrival times between jumps are usually assumed as random variables which are exponentially distributed. In this paper, the inter-arrival times are treated as fuzzy variables with arbitrary distributions. Furthermore, the fuzzy expected value model is established to maximize the expected discounted net return from R&D project. To solve the model, the fuzzy simulation is designed to estimate the value of objective function and the simultaneous perturbation stochastic approximation (SPSA) algorithm is employed to find the optimal solution. Finally, an illustrative numerical example is given.