A novel self-organizing complex neuro-fuzzy approach to the problem of time series forecasting

A self-organizing complex neuro-fuzzy intelligent approach using complex fuzzy sets (CFSs) is presented in this paper for the problem of time series forecasting. CFS is an advanced fuzzy set whose membership function is characterized within a unit disc of the complex plane. With CFSs, the proposed complex neuro-fuzzy system (CNFS) that acts as a predictor has excellent adaptive ability. The design for the proposed predictor comprises the structure and parameter learning stages. For structure learning, the FCM-Based Splitting Algorithm for clustering was used to determine an appropriate number of fuzzy rules for the predictor. For parameter learning, we devised a learning method that integrates the method of particle swarm optimization and the recursive least squares estimator in a hybrid and cooperative way to optimize the predictor for accurate forecasting. Four examples were used to test the proposed approach whose performance was then compared to other approaches. The experimental results indicate that the proposed approach has shown very good performance and accurate forecasting.