General function approximation of a class of cascade chaotic fuzzy systems

Abstract

This paper presents an innovative architecture called cascade chaotic fuzzy system (CCFS) for the function approximation and chaotic modeling. The proposed model can dominate complications in the type-2 fuzzy systems and increase the chaotic performance of a whole framework. The proposed cascade structure is based on combining two or more one-dimensional chaotic maps. The combination provides a new chaotic map with more high nonlinearity than its grain maps. The fusion of cascade chaotic structure into the neurons of the membership layer of a conventional fuzzy system makes the CCFS more capable of confronting nonlinear problems. Based on the General Function Approximation and Stone-Weierstrass theorem, we show that the proposed model has the function approximation property. By analyzing the bifurcation diagram and applying the CCFS to the problem of chaotic modeling, the new model is investigated. Simulation results and analysis are demonstrated to illustrate the concept of general function approximation.