Neural Network Architecture of Fuzzy Systems

Abstract

The paper deals with representations of fuzzy systems by means of neural networks. Two different kinds of neural networks are employed for fuzzy systems modeling. One approach applies feed-forward neural networks which are similar to the well known architecture of a multi-layer perceptron. Another one is based on the equivalence of fuzzy systems and radial basis function neural networks. The two approaches are compared taking into account the assumptions needed to perform a role of a fuzzy system by a neural network. More general representations of fuzzy systems by neural network architectures, which are called fuzzy inference neural networks, are described at first. It is shown that a special case of these networks can be presented in the form of the radial basis function neural network as well as the multi-layer perceptron architecture. The neural network representations of fuzzy systems with singleton and non-singleton fuzzifier are depicted in this paper.