Approximation of fuzzy functions by regular fuzzy neural networks

In this paper, we investigate the ability of regular fuzzy neural networks to provide approximations to fuzzy functions. Since the operation of regular fuzzy neural networks is based on Zadehʹs extension principle, we first present a level characterization of the Zadehʹs extensions of level-continuous fuzzy-valued functions and consider the continuity of these extensions. On the basis of this, we give characterizations of fuzzy functions which can be approximated by a class of four-layer regular fuzzy neural networks according to supremum-metric and level convergence.