FUZZY NEURAL NETWORKS ARE UNIVERSAL APPROXIMATORS
Thomas Feuring, W.-M. Lippe · 1995
. In this paper we examine the capacity of fuzzy neural networks. These networks are multilayer feedforword nets whose processing elements -- the formal neurons -- operate on fuzzy numbers instead of real numbers. We show that these fuzzy neural networks can approximate fuzzy continuous real functions on a compact domain to any degree of accuracy. 1. Introduction It is well known that multilayer neural networks are universal approximators [2] [4]. But do fuzzy neural networks have the same approximation capacity ? J. Buckley and Y. Hayashi presented a function which cannot be approximated by a fuzzy neural network [1], so they argue that fuzzy neural networks are no universal approximators. In this paper we show that fuzzy neural networks can approximate any fuzzy continuous real function on a compact domain to any degree of accuracy. The reason for these contradictory results are different definitions of fuzzy functions. J. Buckley and Y. Hayashi used a very general definition wherea...