Approximation Capabilities And Constructions Of Polygonal Fuzzy Neural Networks

A fuzzy neural network is an organic combination of an artificial neural network and fuzzy techniques that forms a mixable intelligent system with both intelligent information processing and adaptability. As a particular type of pure fuzzy system, fuzzy neural networks can effec-tively handle natural language messages. In the real world, there are more data messages of digital type than language messages. Thus, we may obtain data messages with corresponding input-output relationship of a fuzzy system by measurement date and transmission. According to the contents, this paper is divided into three chapters:In the first chapter, it introduces the background, the present research situation of fuzzy neural networks at home and abroad and the preliminaries.In the second chapter, the concepts of the inductive operators and K-quasi-additive in-tegrals are introduced, and by using integrals transformation theorem, the approximation of regular fuzzy neural networks in the sense of K-integral norms to the fuzzy valued simple func-tion class is studied. Then, in the sense of K-integral norms, the universal approximation of regular fuzzy neural networks with respect to a class of integrally bounded fuzzy functions is discussed.In the third chapter. the polygonal fuzzy numbers are introduced to overcome the complex-ity of fuzzy numbers’ operations, and then. we give the method of changing a fuzzy number into a polygonal fuzzy number through an actual example. Furthermore, we discuss their linear op-eration properties and the representation theorem of polygonal fuzzy numbers valued functions. Moreover. by means of the constructing methods of interpolation neural networks, we construct three classes of three-layer polygonal fuzzy neural networks under fuzzy environment. And then. the approximations of the three classes of polygonal fuzzy neural networks with respect to the continuous polygonal fuzzy valued functions are proved. Finally, aiming at a given polygonal fuzzy valued function. we constitute a polygonal fuzzy neural network with an initial value. afterwards. their algorithm as well as realization process are presented.