Chapter 8 - Fuzzy Neural Networks

Abstract

This chapter presents a new refined classification of fuzzy neural networks (FNNs). This classification conforms to the nature of the processed information and to the corresponding mathematical fields: fuzzy arithmetic and fuzzy logic. Fuzzy arithmetic neurons (FANs) are the basic building blocks of fuzzy arithmetic neural networks (FANNs). The basic building blocks of fuzzy logic-based FNNs are neurons with fuzzy logic (FL), termed as fuzzy logic neurons (FLNs). A sound model of the single neuron is considered to be essential for the development of any more complicated network structures. A considerable part of the chapter is devoted to the development and description of various models of fuzzy neurons. Several novel techniques for fuzzy arithmetic and FL computations in the FNNs are also discussed in the chapter. Two distinctive aspects have been found among these models. First, they can be classified, with respect to the mathematical tools used, into three groups: crisp neurons, fuzzy arithmetic neurons, and FLNs. Second, there are two families of the confluence operations in each of the three groups: product-based, and distance-based. The knowledge presented in the chapter is the outcome of recent endeavors to build a solid basis for FNNs. This field is not settled yet, and it contains many controversies and confusions. The definition of fuzzy neurons and examination of their capabilities are regarded as the first step in building the theory of fuzzy neural nets.