On the dynamical modeling with neural fuzzy networks

In the literature, researchers have introduced delay feedback (or recurrent) networks and claimed that those networks could accurately model dynamical systems without knowing their system orders. In this paper, we have studied those delay feedback networks and also proposed a better version of delay feedback neural-fuzzy networks, called additive delay feedback neural-fuzzy networks (ADFNFN). From our simulations for various examples, it is clearly evident that ADFNFN can have the best modeling accuracy among those existing delay feedback networks. Nevertheless, we also showed by examples that those delay feedback networks can only reach the accuracy of nonlinear autoregressive with exogenous inputs (NARX) models with order two, and that the number of delays in delay feedback networks plays the same role as the order in NARX models.