Abstract: In this paper, by considering the imprecise nature of the parameters in real-word problems, job shop scheduling problems with fuzzy processing time and fuzzy due date are formulated. The uncertainty processing time of operations is described by six-point fuzzy number and the due date is described by trapezoid fuzzy number, then the satisfaction-degree is presented and the formulated job shop scheduling problems are interpreted so as to maximize the average satisfaction-degree index. On the basis of the fuzzy cut, a stability measure is presented to evaluate the stability of the optimal solutions by solving the fuzzy job shop scheduling problems. Through the experimental results, the optimal solutions by solving the formulated model in this paper have the better stability measure.

Key words: six-point fuzzy number, trapezoid fuzzy number, satisfaction-degree, fuzzy cut, stability

摘要： 针对生产环境中调度参数的不确定性，研究含模糊加工时间和模糊交货期的Job Shop调度问题，用6点模糊数表示加工时间梯形模糊数表示交货期。基于隶属度定义工件交货满意度，以最大化平均工件交货满意度作为优化目标建立模糊调度数学模型。基于模糊截集概念设计稳定性指标评价优化方案的稳定性，最后通过仿真结果证明所设计模型能够获得稳定性较好的满意调度方案。

关键词: 6点模糊数, 梯形模糊数, 交货满意度, 模糊截集, 稳定性