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Accurate prediction to the uncertain demand is an important guarantee for preparing the optimal purchasing decision and reducing the inventory cost. Compared with the method of fitting the uncertain demand of commodity sensitive to time and season by general random probability distribution, the fuzzy mathematical method has less relative error and better goodness of fit. Therefore, the fuzzy mathematical method is used for forming the optimal purchasing decision model under uncertain demand. A numerical computation method based on the browsed exact analytic calculation method and two improved PSO algorithm is designed. A plurality of confirmatory experiments and comparative experiments analyze and compare the performance of algorithms with different properties and discus the disadvantages and adaptability thereof, providing new angle and thought for the theoretical research and providing reference basis for the method selection of enterprise.

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