NCFS: new chaotic fuzzy system as a general function approximator

Abstract

Conventional fuzzy systems (type-1 and type-2) are universal approximators. The goal of this paper is to design and implement a new chaotic fuzzy system (NCFS) based on the Lee oscillator for function approximation and chaotic modelling. NCFS incorporates fuzzy reasoning of the fuzzy systems, self-adaptation of the neural networks, and chaotic signal generation in a unique structure. These features enable the structure to handle uncertainties by generating new information or by chaotic search among prior knowledge. The fusion of chaotic structure into the neurons of the membership layer of a conventional fuzzy system makes the NCFS more capable of confronting nonlinear problems. Based on the GFA and Stone-Weierstrass theorems, we show that the proposed model has the function approximation property. The NCFS performance is investigated by applying it to the problem of chaotic modelling. Simulation results are demonstrated to illustrate the concept of function approximation.