Fuzzy-arithmetic-based approach for extracting positive and negative linguistic rules from trained neural networks

Our method extracts linguistic rules from trained neural networks for high-dimensional pattern classification problems with continuous attributes. Characteristic features of our rule extraction method are as follows: (I)It can extract fuzzy if-then rules with linguistic interpretation. Extracted fuzzy if-then rules are always linguistically interpretable. (2) It can handle existing feedforward neural networks that have already been trained. Neither specific learning algorithms nor tailored network architectures are assumed. It does not change weight values of the trained neural networks during the rule extraction process. (3) It is based on fuzzy arithmetic. Linguistic values such as "small" and "large" are presented to neural networks, and corresponding fuzzy outputs are calculated by fuzzy arithmetic for extracting linguistic rules. (4) Negative linguistic rules can be extracted from trained neural networks as well as positive rules. After briefly describing our method, we discuss the accuracy of fuzzy arithmetic and show subdivision methods for decreasing the excess fuzziness in fuzzy outputs from neural networks. We also discuss the handling of negative linguistic rules such as "If x/sub 1/ is small and x/sub 2/ is not large then Class 3" and "If x/sub 1/ is large then not Class 2".