Improvement on the approximation bound for fuzzy-neural networks clustering method with gaussian membership function

Authors:
Weimin Ma;Guoqing Chen
Affiliations:
School of Economics and Management, Tsinghua University, Beijing, P.R. China;School of Economics and Management, Tsinghua University, Beijing, P.R. China
Venue:
ADMA'05 Proceedings of the First international conference on Advanced Data Mining and Applications
Year:
2005

Citing 8
Cited 2

Original Contribution: Approximation of continuous functions on Rd by linear combinations of shifted rotations of a sigmoid function with and without scaling

Neural Networks
Error bounds for approximation with neural networks

Journal of Approximation Theory
An on-line algorithm for creating self-organizing fuzzy neural networks

Neural Networks
Neural networks for optimal approximation of smooth and analytic functions

Neural Computation
Approximation accuracy of some neuro-fuzzy approaches

IEEE Transactions on Fuzzy Systems
Comparison of worst case errors in linear and neural network approximation

IEEE Transactions on Information Theory
Approximation bounds for smooth functions in C(Rd) by neural and mixture networks

IEEE Transactions on Neural Networks
Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks

IEEE Transactions on Neural Networks

Approximation accuracy of table look-up scheme for fuzzy-neural networks with bell membership function

ICONIP'06 Proceedings of the 13th international conference on Neural information processing - Volume Part III
Approximation bound for fuzzy-neural networks with bell membership function

FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part I

Quantified Score

Hi-index	0.00

Visualization

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.