Type-1 recurrent intuitionistic fuzzy functions for forecasting

Abstract

In this study, a novel forecasting method that employs intuitionistic fuzzy c-means clustering and a grey wolf optimizer in recurrent type-1 fuzzy functions (R-T1FFs) is introduced. R-T1FFs, which adapt to the moving average (MA) along with an autoregressive model (AR), were introduced recently to improve the forecasting performances of type-1 fuzzy functions, which adapted solely to the AR model. Because the objective function of R-T1FFs was non-derivative, particle swarm optimization was used to estimate the coefficients of the model. Because R-T1FFs calculate the disturbance terms for the MA model recursively, the model is computationally intensive. Therefore, the proposed method employs a grey wolf optimizer for training processes. Examples in the literature demonstrate that the grey wolf optimizer performs well when obtaining model coefficients because convergence is faster owing to a continuous reduction in the search space and reduced storage requirements. Another contribution of the proposed method is an improved forecasting accuracy, which is obtained by quantifying the hesitancy with which an observation belongs to a cluster given a certain degree of membership. A comparison of the proposed method with numerous existing methods is conducted for 12 practical time series datasets as applications. The accuracy of the proposed method is investigated using root-mean-squared error, mean absolute percentage error, and correlation coefficients; further, whether it produces significantly better outcomes than the existing methods is verified using paired t-tests. For example, it is clear by looking at the average RMSEs of the methods that the best forecasting performance is produced by the proposed method for Taiwan stock exchange datasets. (C) 2019 Elsevier Ltd. All rights reserved.