Chaotic time series prediction via artificial neural square fuzzy inference system

• We showed that high order TSK fuzzy systems are general approximators.
• We introduced a simplified type of second order TSK system.
• The possibility of training those systems by ANFIS is investigated.
• A new method is developed for training the proposed second order TSK system.
• The efficiency of this method is investigated by comparing with other methods.

The present article investigates the application of second order TSK (Takagi Sugeno Kang) fuzzy systems in predicting chaotic time series. A method has been introduced for training second order TSK fuzzy systems using ANFIS (Artificial Neural Fuzzy Inference System) training method. In a second order TSK system existence of nonlinear terms in the rules’ consequence prohibits use of current available ANFIS codes as is but the proposed method makes it possible to use ANFIS for a class of simplified second order TSK systems. The main impact of this method on the expert and intelligent systems is to provide a new way for modeling and predicting the future situation of more complex phenomena with a smaller decision rule base. The most significance of the proposed method is the simplicity and available code reuse property. As a case study the proposed method is used for the prediction of chaotic time series. Error comparison shows that the proposed method trains the second order TSK system more effectively.