Consistent Sobolev regression via fuzzy systems with overlapping concepts

In this paper we propose a new nonparametric regression algorithm based on fuzzy systems with overlapping concepts. We analyze its consistency properties, showing that it is capable to reconstruct an infinite-dimensional class of function when the size of the noisy dataset grows to infinity. Moreover, convergence to the target function is guaranteed in Sobolev norms so ensuring uniform convergence also for a certain number of derivatives. The connection with regularization networks, Bayesian estimation and Tychonov regularization is highlighted.