Choice of the radial basis function approximation in neural networks used for fuzzy system implementation

Abstract

The paper investigates the method proposing a fuzzy system implementation through its approximation with neural networks. This method allows an easy and cheap realisation on simple general purpose microprocessors popular with the industry. This paper concentrates on further simplification of realisation by the replacement of Gaussian radius basis function in neural networks with its linear and piecewise linear approximation. Different approximating possibilities are tested on four controllers chosen as benchmarks. The analysis has identified that the Gaussian basis function can be approximated without a significant change of error if the number of neurons is not too small.