Chaotic time series prediction using ELANFIS

This paper investigates the performance of Adaptive Neuro-Fuzzy Inference System (ANFIS) and Extreme Learning ANFIS (ELANFIS) in the chaotic time series prediction problem. ELANFIS is one of the neuro-fuzzy systems, which combines the learning capabilities of extreme learning machine (ELM) and the explicit knowledge of the fuzzy systems. In ELANFIS, premise parameters are randomly generated with some constraints to accommodate fuzziness, whereas consequent parameters are identified analytically using Moore-Penrose generalized inverse. Two benchmark problems, Mackey Glass equation and Lorenz equation, are used to compare the performance measures of the two algorithms. It has been shown that when the complexity of the model is increased the performance of ELANFIS is better than ANFIS because of the much lower training time required.