Nonparametric learning capabilities of fuzzy systems

Abstract

Nonparametric estimation capabilities of fuzzy systems in stochastic environments are analyzed in this paper. By using ideas from sieve estimation, increasing sequences of fuzzy rule-based systems, capable of consistently estimating regression surfaces in different settings, are constructed. Results include least squares learning of a mapping perturbed by additive random noise in a static-regression context and least squares learning of a regression surface from data generated by a bounded stationary ergodic random process. 1 L estimation is also studied, and the consistency of fuzzy rule-based sieve estimators for the 1 L - optimal regression surface is shown, thus giving additional theoretical support to the robust filtering capabilities of fuzzy systems and their adequacy for modeling, prediction and control of systems affected by impulsive noise.