Optimization of interval type-2 fuzzy integrators in ensembles of ANFIS models for prediction of the Mackey-Glass time series

This paper describes the optimization of interval type-2 fuzzy integrators in Ensembles of ANFIS (adaptive neurofuzzy inferences systems) models for the prediction of the Mackey-Glass time series. The considered a chaotic system is the Mackey-Glass time series that is generated from the differential equations, so this benchmark time series is used to the test of performance of the proposed ensemble architecture. We used the interval type-2 and type-1 fuzzy systems to integrate the output (forecast) of each Ensemble of ANFIS models. Genetic Algorithms (GAs) were used for the optimization of membership function parameters of each interval type-2 fuzzy integrators. In the experiments we optimized Gaussian, Generalized Bell and Triangular membership functions parameter for each of the fuzzy integrators, thereby increasing the complexity of the training. Simulation results show the effectiveness of the proposed approach.