Decreasing excess fuzziness in fuzzy outputs from neural networks for linguistic rule extraction

Ishibuchi et al. (1996) have proposed a linguistic rule extraction method from trained neural networks for pattern classification problems. In the method, antecedent linguistic values such as "small" and "large" are used as inputs to a multilayer feedforward neural network for determining the consequent part of linguistic rules. Since the linguistic input values are handled as fuzzy numbers, the corresponding outputs from the neural network are also calculated as fuzzy numbers by fuzzy arithmetic. The accurate calculation of the fuzzy outputs is very important because the determination of the consequent part is based on the calculated fuzzy outputs. It is, however, well-known that fuzzy arithmetic involves excess fuzziness. In this paper, we illustrate how subdivision methods can decrease the excess fuzziness. We also examine the effect of those methods on the performance of our rule extraction method.