Fuzzy Inference and Application to Industrial Engineering

在工业工程领域，由于许多问题涉及到基于人类用户决策、评价和判断的不确定性，因此常规优化技术的应用并非易事。在这个项目中，我们试图使用可能性分布和模糊数来表示不确定性，以数学方式处理这些问题。我们研究了投资组合选择、模式分类和调度。对于投资组合选择，我们建立了一个可能性投资组合选择问题，其中每个投资项目的预期收益由一个可能性分布表示。在模式分类方面，我们提出了一种语言分类规则的自动生成方法，该方法的前置部分涉及“小”和“大”等语言值。每个语言值的意义由模糊数的隶属函数来表示。然后，我们提出了一种基于遗传算法的方法来选择少量有意义的语言学家…从大量生成的规则中获得更多的IC规则。神经网络也被用来生成模式分类问题的语言规则。将神经网络的连接权、输入和目标扩展为模糊数，以便以与数值数据相同的方式处理语言数据。对于调度问题，引入了两种不确定性。一个是与决策者对每项工作的完成时间的满意度相关的不确定性。另一个是每台机器上每个作业的加工时间的不确定性。引入模糊交货期的概念来表示决策者对完工时间的满意度。在此基础上，建立了两个基于模糊交货期的模糊调度问题：总满意度最大化和最低满意度最大化。通过用模糊数表示每个作业在每台机器上的不确定加工时间，我们还建立了另一类模糊调度问题。较少

In the field of industrial engineering, the application of conventional optimization techniques is not easy because many problems involve uncertainty based on the decision making, evaluation and judgment by human users. In this project, we tried to mathematically handle those problems using possibility distributions and fuzzy numbers for denoting the uncertainty. We studied portfolio selection, pattern classification and scheduling. For portfolio selection, we formulate a possibilistic portfolio selection problem where the expected return from each investment item is represented by a possibility distribution. For pattern classification, we propose an automatic generation method of linguistic classification rules whose antecedent parts involve linguistic values such as "small" and "large". The meaning of each linguistic value is specified by the membership function of a fuzzy number. Then we proposed a genetic-algorithm-based approach for selecting a small number of significant linguist … More ic rules from large number of generated rules. Neural networks were also employed to generate linguistic rules for pattern classification problems. Connection weights, inputs and targets of neural networks were extended to fuzzy numbers in order to handle linguistic data in the same manner as numerical data. For scheduling problems, two kinds of uncertainty was introduced. One is the uncertainty related to the satisfaction of the decision maker for the completion time of each job. The other is the uncertainty of the processing time of each job at each machine. We introduced the concept of the fuzzy due-date for representing the satisfaction grade of the decision maker for the completion time. Then we formulated two fuzzy scheduling problems based on the fuzzy due-date : maximization of the total satisfaction grade and maximization of the minimum satisfaction grade. We also formulated another kind of fuzzy scheduling problems by representing the uncertain processing time of each job at each machine by a fuzzy number. Less