Genetic Optimization of Type-1 and Interval Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction

摘要

This paper describes the Mackey-Glass time series prediction using genetic optimization of type-1 and interval type-2 fuzzy integrators in Ensembles of adaptive neuro-fuzzy inferences systems (ANFIS) models, with emphasis on its application to the prediction of chaotic time series. The considered chaotic problem 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 outputs (forecasts) of each of the ANFIS models in the Ensemble. Genetic algorithms (GAs) were used for the optimization of memberships function (with linguistic labels "Small, Middle, and Large") parameters of the fuzzy integrators. In the experiments, the GAs optimized the Gaussians, generalized bell and triangular membership functions for each of the fuzzy integrators, thereby increasing the complexity of the training. Simulation results show the effectiveness of the proposed approach.