Analysis and design of time-variant fuzzy systems based on dynamic fuzzy inference

In this paper, a class of time-variant fuzzy systems is designed and analyzed. Firstly, a novel model of dynamic fuzzy inference (DFI) is proposed, and the corresponding DFI method is obtained. Then, the response abilities of time-variant fuzzy systems constructed by the DFI method are analyzed. Some sufficient conditions for time-variant fuzzy systems as step functions, fitted functions and interpolation functions are derived. Furthermore, a sufficient and necessary condition for time-variant fuzzy systems as interpolation functions is also deduced. In addition, the approximation problem of time-variant fuzzy systems is discussed. It is proved that time-variant fuzzy systems constructed by the DFI method are universal approximators to a class of nonlinear systems. In addition, the approximation accuracy of the corresponding time-variant fuzzy systems is investigated. Finally, a simulation experiment is provided to demonstrate how to design a time-variant fuzzy system in order to approximate a given nonlinear system to a desired accuracy.