Development of Fuzzy Systems with Learning Capability

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Although training of neural networks is slow and analysis of the trained networks is difficult, they have high generalization ability for a wide range of applications. On the contrary, fuzzy systems are easily analyzed using fuzzy rules but it is difficult to obtain fuzzy rules and generalization ability of fuzzy systems is inferior to that of neural networks. Thus our research target was to develop fuzzy systems with faster training capability and higher generalization ability. The research results are summarized as follows :1.Dynamic training architecture of a fuzzy classifier with ellipsoidal regions was developed. Initially for each class one fuzzy rule is defined. Then if the recognition rate of the classifier is not sufficient, fuzzy rules are defined using the misclassified data. By this dynamic architecture, the generalization ability of the classifier was improved for the data set with discrete inputs.2.By the Cholesky factorization and skipping the near zero elements in calculating the membership functions of the fuzzy classifier with ellipsoidal regions, two to seven times speed-up was obtained for the bench mark data. When the number of data is smaller than that of input variables, the generalization ability is improved by controlling the singular values.3.Since the fuzzy classifier with ellipsoidal regions is based on the Mahalanobis distance, it is shown to be invariant to linear transformation of input variables.4.Fuzzy function approximators were developed by extending the fuzzy classifier with ellipsoidal regions and their usefulness was demonstrated for the water purification plant.