Universal Approximation Analysis Of Generalized Hierarchical Hybrid Fuzzy Systems

Based on the connected piecewise linear function and the regular fuzzy neural networks, the universal approximation of the generalized hierarchical hybrid fuzzy systems is studied. Mean-while, we design the fuzzy learning algorithm of the universal approximation, which plays a theoretical foundation for the application of soft computing technology.This thesis consists of three primary parts:Part one introduces some original background of the title, some preliminaries and situations of the present researches.Part two is mainly contributed to universal approximation analysis of regular fuzzy neural networks. First of all. the multi-variable continuous functions class is extended as a functions class of preserving maximum values in fuzzy neural networks, and the properties of extended functions class on compact sets are studied by means of the concept of preserving maximum values. What’s more, it is discussed that three-layer regular fuzzy neural networks possess the approximation with respect to the extended fuzzy function class. Furthermore, the approxima-tion performance between the expect output and the real output of forward regular fuzzy neural networks is analyzed and textual researched by a simulated example.Part third focuses on the universal approximation analysis of generalized hierarchical hybrid fuzzy systems. Firstly, the conception of square pricewise linear function and K-Quasi-additive integral are introduced. In the meanwhile, by using the excellent properties of induced opera-tor, it is discussed that square pricewise linear functions possess universal approximation for a class of integrally bounded functions in the sense of integral norm. Secondly, on the basis of the Mamdani fuzzy system and the T-S fuzzy system, the generalized hierarchical hybrid fuzzy systems are established by introducing a parameter η. In addition, the equivalence of hierarchy or not of this kind of hybrid fuzzy systems is proved, and then the "rules explosion" of general-ized fuzzy systems can be avoided in theory. Finally, the universal approximation of generalized hierarchical hybrid fuzzy systems is studied in the sense of integral norms by means of the connected piecewise linear functions, and we get some important conclusions. Moreover, tak-ing advantage of two simulation examples. we study their approximation and realization process.