Analysis Of Stability Of Polygonal Fuzzy Neural Network And Approximation Of Stochastic Hybrid Fuzzy System

Polygonal fuzzy neural networks accomplish the fuzzy information processes by determined the finite nodes of polygonal fuzzy numbers, and their expressions base on the arithmetic operation system of polygonal fuzzy numbers. Through metering data or digital sensor, fuzzy system obtains data information which react the input and output of the system. Although neither of them relies on an accurate mathematical model, both of them have the ability of logical reasoning, numerical calculation and approximation capability of nonlinear function. Based on the stability of polygonal fuzzy neural network and the approximation of stochastic hybrid fuzzy system, this article carries out the theoretical analysis and algorithm research. The concrete research content as follows:Part one:some original backgrounds of the title, some research status are introduced.Part two:the stability analysis of polygonal fuzzy neural network. On the one hand, we put forward the concepts of the maximum perturbation error of polygonal fuzzy numbers, perturba-tion of training pattern pairs, and design the learning algorithm of connection weight according to error-correction rules. On the other hand, whenever the transfer function satisfied the Lipschitz condition and the training pattern pairs occur perturbation, the changes in the polygonal fuzzy neural networks output are discussed, furthermore, the perturbation of this network with respect to the training pattern pairs possesses the global stability is proved. Moreover, the influence of perturbations of training pattern pairs on the stability of polygonal fuzzy neural networks is ex-plained by the simulative examples.Part three:the approximation analysis of stochastic hybrid fuzzy system. Firstly, according to the properties of stochastic measure and stochastic integral, the canonical representation of a stochastic process with orthogonal increments is given. Secondly, on the basis of the stochastic Mamdani fuzzy system and the stochastic T-S fuzzy system, the stochastic parameters are utilized to established to stochastic hybrid fuzzy system. Furthermore, the approximation of stochastic hybrid fuzzy system is studied in the sense of mean square based on the canonical representation of stochastic process. Finally, aiming at a given weakly stationary process in the simulation exam-ple, we derive from the learning algorithm of the stochastic hybrid fuzzy system, meanwhile, by comparing the image simulation of the covariance function, the approximation in the mean square and its realization is illustrated.