On maximum likelihood fuzzy neural networks

Abstract

In this paper, M-estimators, where M stands for maximum likelihood, used in robust regression theory for linear parametric regression problems will be generalized to nonparametric maximum likelihood fuzzy neural networks (MFNNs) for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general nonlinear learning problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) will be derived. Some numerical examples will be provided to compare the robustness against outliers for usual fuzzy neural networks (FNNs) and the proposed MFNNs. Simulation results show that the MFNNs proposed in this paper have good robustness against outliers.