The Fuzzy Neural Networks Based On SAM Systems

The standard additive model (SAM) was proposed by Bart Kosko who is a professor of electrical engineering at the University of Southern California in 199l.Kosko introduced the idea of additive fuzzy systems in a simple algebraic form that is the standard additive model in the book of "Fuzzy Engineering" in 1996. The feedforward standard additive model is the most important special case of an additive fuzzy system and it is an important new framework for fuzzy systems. Kosko applied it to several engineering applications and summarized that the key of fuzzy engineering was function approximation in the book of Fuzzy Engineering.Since fuzzy neural networks have several features that make them well suit to wide range of knowledge engineering applications. In this paper,we introduce a new architecture,which stands for Fuzzy Neural Network on the base of the standard additive model,and investigate some learning and adaptation strategies associated with the fuzzy sets. Because the choice of fuzzy set functions affects how well a fuzzy system approximates a function and Gaussian bell-curve sets give richer fuzzy systems with simple learning laws,we choose Gaussian function set as fuzzy set functions. The Gaussian function set depends on its centroid and width,therefore,we derive new supervised gradient descent algorithms to tune the parameters of "if-part" of Gaussian functions. It also tunes the "then-part"of Gaussian function. Learning tends to move the rule patches among the bumps,so we can get better approximation efficient.On the basis of this study,a simulation example of nonlinear function model is shown in the end .The simulation shows that the algorithms we propose are efficient and correct.