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 arbitrary regression surfaces are constructed. Results include least squares learning of a mapping perturbed by additive random noise in a static-regression context. L1 (i.e., least absolute deviation) estimation is also studied, and the consistency of fuzzy rule-based sieve estimators for L1-optimal regression surfaces 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.