Publication details

Reference

G. Ferrari-Trecate and R. Rovatti. Consistent Sobolev regression via fuzzy systems with overlapping concepts. Fuzzy Sets and Systems , 157(8):1075--1091, 2006.

Abstract

In this paper we propose a new nonparametric regression algorithmbased on Fuzzy systems with overlapping concepts. We analyze itsconsistency properties, showing that it is capable to reconstructan infinite-dimensional class of function when the size of thenoisy dataset grows to infinity. Moreover, convergence to thetarget function is guaranteed in Sobolev norms so ensuring uniformconvergence also for a certain number of derivatives. Theconnection with Regularization Networks, Bayesian estimation andTychonov regularization is highlighted.