Fuzzy Inference and Application to Industrial Engineering

在工业工程领域，传统优化技术的应用并不容易，因为许多问题涉及基于人类用户决策、评估和判断的不确定性。在这个项目中，我们试图用可能性分布和模糊数来表示不确定性，从数学上处理这些问题。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，我们提出了一个可能性投资组合选择问题，其中每个投资项目的期望收益由可能性分布表示。在模式分类方面，提出了一种语言分类规则的自动生成方法，该规则的先行项包含“小”和“大”等语言值。每个语言值的含义由模糊数的隶属函数表示。然后，我们提出了一种基于遗传算法的方法，从大量生成的规则中选择少量重要的语言规则。神经网络也被用于生成语言规则的模式分类问题。将神经网络的连接权值、输入和目标扩展为模糊数，以便像处理数值数据一样处理语言数据。对于调度问题，引入了两种不确定性。一是与决策者对每项工作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处理时间的不确定性。我们引入模糊截止日期的概念来表示决策者对完成时间的满意程度。在此基础上，提出了基于模糊到期日的两个模糊调度问题：总满意度最大化和最小满意度最大化。通过用模糊数表示每台机器上每个作业的不确定加工时间，提出了另一类模糊调度问题。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