Fuzzy systems with overlapping Gaussian concepts: Approximation properties in Sobolev norms

In this paper the approximating capabilities of fuzzy systems with overlapping Gaussian concepts are considered. The target function is assumed to be sampled either on a regular gird or according to a uniform probability density. By exploiting a connection with Radial Basis Functions approximators, a new method for the computation of the system coefficients is provided, showing that it guarantees uniform approximation of the derivatives of the target function