Improvement on the approximation bound for fuzzy-neural networks clustering method with Gaussian Membership Function

Abstract

A great deal of research has been devoted in recent years to the designing Fuzzy-Neural Networks (FNN) from input-output data. And some works were also done to analyze the performance of some methods from a rigorous mathematical point of view. In this paper, a new approximation bound for the clustering method, which is employed to design the FNN with the Gaussian Membership Function, is established. It is an improvement of the previous result in which the related approximation bound was somewhat complex. The detailed formulas of the error bound between the nonlinear function to be approximated and the FNN system designed based on the input-output data are derived. © Springer-Verlag Berlin Heidelberg 2005.