Optimized cascade chaotic fuzzy system (OCCFS) and its application to function approximation and chaotic systems identification

To overcome the limitations of classic fuzzy systems, including Type-1 and Type-2 fuzzy systems, and to propose a robust and flexible intelligent network, this paper presents a new fuzzy system called optimized cascade chaotic fuzzy system (OCCFS) for the function approximation and chaotic systems identification. The OCCFS incorporates fuzzy reasoning of the fuzzy systems, self-adaptation of the neural networks, chaotic signal generation, and generalizability of cascade systems in a unique structure. These features are integrated and optimized with the evolutionary algorithm to present the best performance. In fact, after generating chaotic properties in the neuronal oscillation model, the cascade structure is used for enhancing it and forwarding it to the inference engine of the fuzzy model. The proposed cascade structure could enhance the chaotic properties of primary functions. In other words, outstanding results of Type-2 fuzzy systems (T2FSs) can be achieved through Type-1 fuzzy systems (T1FSs). Based on the General Function Approximation and Stone-Weierstrass theorem, we show that the proposed model has the function approximation property. The prediction capability of the proposed model is verified through popular simulated and real benchmark problems. Moreover, the OCCFS is applied to predict the traffic flow in Ferdowsi Street, Mashhad city, Khorasan Province, Iran. In comparison with T1FS and T2FS, and according to the criteria of accuracy and time, the proposed model provides more accurate and robust results.