Fuzzy Inference Systems and Fuzzy Neural Networks

Abstract

In recent years, the attention of many researchers in the field of artificial intelligence systems attracts the problem of decision making under uncertainty, the incompleteness of the initial data and quality criteria. There is a new trend in the theory of complex decision-making, which is rapidly developing—making decisions under uncertainty. A promising approach for solving many decision-making problems under uncertainty and incomplete information is based on fuzzy sets and systems theory created by Zadeh [1]. The introduction by L. Zadeh of the concept of linguistic variables described by fuzzy sets [2] gave rise to a new class of systems—fuzzy logic systems (FLS), which allows to formalize fuzzy expert knowledge. The use of fuzzy inference systems (FIS) and built on the their basis fuzzy neural networks (FNN) has allowed to solve many problems of decision-making under uncertainty, incompleteness and qualitative information—forecasting, classification, cluster analysis, pattern recognition. This chapter is devoted to the detailed consideration of FL systems. It discusses the basic algorithms of fuzzy inference Mamdani, Tsukamoto, Larsen and Sugeno (Sect. 3.2). In Sect. 3.3 the methods of defuzzification are described. In the Sect. 3.4 the important Fuzzy approximation theorem (FAT-theorem) is considered which is theoretical ground for wide applications of FNN. Further fuzzy controller (FC) Mamdani and Tsukamoto and classical learning algorithm on the basis of back-propagation are detailly considered. A new learning algorithm of FC Mamdani and Tsukamoto for Gaussian membership functions (MF) of gradient type is described (Sect. 3.6). Next FNN ANFIS is considered, its architecture and gradient learning algorithm are presented (Sect. 3.7). Then FNN TSK, the development of FNN ANFIS, is described and its hybrid training algorithm is reviewed (Sect. 3.8). In the Sect. 3.9 adaptive wavelet-neuro-fuzzy networks are considered and different learning algorithms in batch and on-line mode are presented. Cascade neo-fuzzy neural networks (CNFNN) are considered, training algorithms are presented and GMDH method for its structure synthesis is described and analyzed (Sect. 3.10).