A study and development of high-order fuzzy time series forecasting methods for air quality index forecasting

The endless adverse effects of air pollution incidents have raised significant public concerns in the past few decades. The measure of air pollution, that is, the air quality index (AQI), is highly volatile and associated with different kinds of uncertainties. Following this, the study and development of accurate fuzzy time series forecasting (TSF) methods for predicting the AQI have a significant role in air pollution control and management. Motivated by this, in this paper, a systematic study is made to evaluate the true potential of fuzzy TSF methods employing traditional fuzzy set (TFS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), and neutrosophic fuzzy set (NFS) in forecasting the AQI. Two novel high-order fuzzy TSF methods, TFS-multilayer perceptron (MLP) and HFS-MLP, are proposed employing TFS and HFS in which ratio trend variation of AQI data is used instead of original AQI, MLP is used to model the fuzzy logical relationships (FLRs), and none/mean of aggregated membership values are used while modeling the FLRs using MLP. The results from the proposed fuzzy TSF methods are compared with recently proposed fuzzy TSF methods employing TFS, IFS, and NFS and six popular machine learning models, including MLP, support vector regression (SVR), Bagging Regressors, XGBoost, long-short term memory (LSTM), and convolutional neural network (CNN). The “Wilcoxon Signed-Rank test” and “Friedman and Nemenyi hypothesis test” are applied to the results obtained by employing different ratios in the train-validation-test to draw decisive conclusions reliably. The simulation results show the statistical dominance of the proposed TFS-MLP method over all other crisp and fuzzy TSF methods employed in this paper.