Fuzzy Inference and Application to Industrial Engineering

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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