Fuzzy Neural Networks -- Basics and New Development

Abstract

In this talk, I shall introduce the basics of Fuzzy Neural Networks (FNNs) and its newest developments. The FNN combines the advantages of neural networks (NN) and fuzzy logic (FL) into one functional mechanism, such that it contains brain-like low-level learning and high-level reasoning capabilities at once. The FNN brings the learning power of NN into FL, and brings the human understandable structure-like knowledge into NN. Hence, the FNN has the advantages of high learning speed and economic network size over the normal NN. We shall then introduce two dedicated FNN models, SONFIN (Self-constructing neural fuzzy inference network) and RSONFIN (Recurrent SONFIN). The former is good at static mapping, and the latter is especially for temporal mapping. The SONFIN (RSONFIN) is inherently a (recurrent) multilayered connectionist network for realizing the basic elements and functions of (dynamic) fuzzy inference. Each weight as well as node in the SONFIN and RSONFIN has its own meaning and represents a special element in a fuzzy rule. There are no hidden nodes (i.e., no membership functions and fuzzy rules) initially in the RSONFIN. They are created on-line via concurrent structure identification (the construction of (dynamic) fuzzy if-then rules) and parameter identification (the tuning of the free parameters of membership functions). The structure learning together with the parameter learning forms a fast learning algorithm for building a small, yet powerful, dynamic FNN. We shall use some examples to demonstrate the power of these two FNNs. Finally, we shall also mention our on-going research topic on applying SVM (Support Vector Machine) to FNN. This FNN can minimize both the empirical risk and the expected risk for a given training and test data set so that a better generalization can be obtained. This will become a new generation of FNN.