Fuzzy Logic and Neuro-fuzzy Systems: A Systematic Introduction

Fuzzy logic is a rigorous mathematical field, and it provides an effective vehicle for modeling the uncertainty in human reasoning. In fuzzy logic, the knowledge of experts is modeled by linguistic rules represented in the form of IF-THEN logic. Like neural network models such as the multilayer perceptron (MLP) and the radial basis function network (RBFN), some fuzzy inference systems (FISs) have the capability of universal approximation. Fuzzy logic can be used in most areas where neural networks are applicable. In this paper, we first give an introduction to fuzzy sets and logic. We then make a comparison between FISs and some neural network models. Rule extraction from trained neural networks or numerical data is then described. We finally introduce the synergy of neural and fuzzy systems, and describe some neuro-fuzzy models as well. Some circuits implementations of neuro-fuzzy systems are also introduced. Examples are given to illustrate the concepts of neuro-fuzzy systems.