Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Fuzzy neural networks: a survey
Fuzzy Sets and Systems
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Selecting fuzzy if-then rules for classification problems using genetic algorithms
IEEE Transactions on Fuzzy Systems
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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.