Basic Structure of Fuzzy Neural Networks

Abstract

In this chapter we shall discuss the structure of fuzzy neural networks. We start with general definitions of multifactorial functions. And we show that a fuzzy neu-ron can be formulated by means of standard multifactorial function. We also give definitions of a fuzzy neural network based on fuzzy relationship and fuzzy neurons. Finally, we describe a learning algorithm for a fuzzy neural network based on V and A operations. 6.1 Definition of Fuzzy Neurons Neural networks alone have demonstrated their ability to classify, recall, and associate information [l]. In this chapter, we shall incorporate fuzziness to the networks. The objective to include the fuzziness is to extend the capability of the neural networks to handle " vague " information than " crisp " information only. Previous work has shown that fuzzy neural networks have achieved some level of success both fundamentally and practically [l-lo]. As indicated in reference [l], there are several ways to classify fuzzy neural networks: (1) a fuzzy neuron with crisp signals used to evaluate fuzzy weights, (2) a fuzzy neuron with fuzzy signals which is combined with fuzzy weights, and (3) a fuzzy neuron described by fuzzy logic equations. In this chapter, we shall discuss a fuzzy neural network where both inputs and outputs can be either a crisp value or a fuzzy set. To do this we shall first introduce multifactorial function [ll, 121. We have pointed out from Chapter 4 that one of the basic functions of neurons is that the input to a neuron is synthesized first, then activated, where the basic operators to be used as synthesizing are " + " and ". " denoted by (+, .) and called synthetic operators. However, there are divers styles operators will be multifactorial functions, so we now briefly introduce the concept of multifactorial functions. In [0, lIm, a natural partial ordering " 5 " is defined as follows: A multifactorial function is actually a projective mapping from an rn-ary space to a