中文摘要：

应用模糊集理论研究了不确定条件下模糊需求、允许缺货、有拖后补定的库存管理问题。基于模糊集理论，给出库存参数的模糊数表达和模型的有关假定，得到每周期单位时间平均利润函数，采用广义平均数表示法进行解模糊并优化求解，在单位时间平均利润最大的标准下，求出每周期最优库存进货批量。最后，通过示例分析，证明了模糊理论处理库存管理问题的实用价值和现实意义。

英文摘要：

The theory of fuzzy set was applied to the inventory management for balanced demand with back order allowed during stock-out. Based on the theory of fuzzy set, the fuzzy number expressions of inventory parameters were given with some assumptions defined, thus obtaining the average profit function per unit time for each cycle. And a fuzzy/optimum solution to the function was derived by means of extended mean value. Then, the optimized backordering quantity of stock replenishment for each cycle was given under conditions that the criterion of average profit per unit time is maximized. An example is given showing the practicality and feasibility of the inventory control to which the fuzzy theory is applied.