Techniques and Applications of Neural Networks for Fuzzy Rule Approximation

Abstract

This chapter discusses neural-network-based methods for approximately realizing fuzzy if–then rules. Inputs and outputs of neural networks are linguistic values such as “small” and “large.” Neural networks are used to approximately realize fuzzy mappings from antecedent linguistic values into consequent linguistic values of fuzzy if-then rules. Neural networks are also used to predict unknown consequent linguistic values for given antecedent linguistic values. The chapter describes three approaches to the implementation of fuzzy if–then rules by neural networks. Two approaches use preprocessors for transforming linguistic values into real vectors in the learning of neural networks. The other approach directly handles linguistic values using fuzzy arithmetic. Advantages and disadvantages of those approaches are then illustrated by computer simulations. The chapter then demonstrates how neural networks could be employed for generating fuzzy if–then rules from sparse rules. Incomplete fuzzy rule bases are completed by fuzzy if­–then rules extracted from trained neural networks. Then the chapter discusses the learning of neural networks from numerical data and linguistic knowledge. These two kinds of information are simultaneously utilized as training data in the learning. Finally, the chapter shows how neural networks could be utilized in classification problems where numerical data and linguistic knowledge are provided.