Learning from Linguistic Rules and Rule Extraction for Function Approximation by Neural Networks

We have already shown that the relation between neural networks and linguistic knowledge is bidirectional for pattern classification problems. That is, neural networks are trained by given linguistic rules, and linguistic rules are extracted from trained neural networks. In this paper, we illustrate the bidirectional relation for function approximation problems. First we show how linguistic rules and numerical data can be simultaneously utilized in the learning of neural networks. In our learning scheme, antecedent and consequent linguistic values are specified by membership functions of fuzzy numbers. Thus each linguistic rule is handled as a fuzzy input-output pair. Next we show how linguistic rules can be extracted from trained neural networks. In our rule extraction method, linguistic values in the antecedent part of each linguistic rule are presented to a trained neural network for determining its consequent part. The corresponding fuzzy output from the trained neural network is calculated by fuzzy arithmetic. The consequent part of the linguistic rule is determining by comparing the fuzzy output with linguistic values. Finally we suggest some extensions of our rule extraction method.