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The main purpose of this study is to construct a suitable research and development (R&D) decision model which would facilitate the analysis of optimal stopping and investment strategy with mixed uncertainty of randomness and fuzziness in R&D project. In classical 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 random fuzzy variables with arbitrary distributions. Furthermore, the random fuzzy expected value model is established to maximize the expected discounted net return from R&D project. To solve the model, the random fuzzy simulation for expected discounted net return is given and embedded into particle swarm optimization (PSO) algorithm to design a hybrid intelligent algorithm. Finally, an numerical example is given for the sake of illustration of the effectiveness of this algorithm.