Time series prediction using ensembles of ANFIS models with genetic optimization of interval type-2 and type-1 fuzzy integrators

Abstract

This paper describes an optimization of interval type-2 and type-1 fuzzy integrators in ensembles of ANFIS models with genetic algorithms (GAs), this with emphasis on its application to the prediction of chaotic time series, where the goal is to minimize the prediction error. The Mackey-Glass time series was considered to validate the proposed ensemble approach. The methods used for the integration of the ensembles of ANFIS are: type-1 and interval type-2 Mamdani fuzzy inference systems (FIS). Genetic Algorithms are used for optimization of the membership function parameters of the FIS in each integrator. In the experiments we changed the type of the membership functions for each type-1 and interval type-2 FIS, thereby increasing the complexity of the training, The output (Forecast) generated by each integrator is calculated with the RMSE (root mean square error) to minimize the prediction error, therefore we compared the performance obtained by each FIS.

Optimization of the Fuzzy Integrators in Ensembles of ANFIS Model for Time Series Prediction: The case of Mackey-Glass

“…One of the chaotic time series data used in many works is defined by the Mackey-Glass [8][9][10][11][12][13] time series, whose in (1) is given by:…”

“…From the Mackey-Glass time series we used 800 pairs of data points ( Fig. 2), similar to [8][9][10]13]. We predict x (t) from three past (delays) values of the time series, that is, x (t-18), x (t-12), and x (t-6).…”

“…The basic principles of genetic algorithms were established by Holland [3,4] and are well described in texts Goldberg [5,6] and Davis [7]. This paper reports the results of the simulations, in which the Mackey-Glass time series [8][9][10][11][12][13] prediction using genetic optimization for the fuzzy integrators in ensembles of ANFIS models. The results for each AN-FIS are evaluated by the metric of the root mean square error (RMSE).…”

Granular computing, computational intelligence, and the analysis of non-geometric input spaces

“…A particularly interesting consequence of this design choice is the fact that a granular neural network typically produces a granular output, hence consistent with the framework chosen for the IGs. Another interesting application of IGs can be cited in higher-order fuzzy inference systems (Biglarbegian et al 2010;Gaxiola et al 2014;Soto et al 2014;Mendel 2014). Fuzzy inference systems and their extensions played a pivotal role in many applications in the last few decades.…”

Maximum and minimum stock price forecasting of Brazilian power distribution companies based on artificial neural networks

“…In this context, intelligent systems, such as Artificial Neural Networks (ANN) [1][2][3][4][5]8,11,12,[16][17][18], Fuzzy Inference Systems [6,9], and NeuralFuzzy Systems [10,13,14,19] are considered useful approaches for addressing problems of time series forecasting.…”