WaveFLSTM: Wavelet-based fuzzy LSTM model for forecasting complex time series data

The forecasting of time series continues to be a prominent area of interest among researchers exploring advanced learning techniques. In recent times, deep recurrent neural networks, particularly long short-term memory (LSTM) models, have demonstrated exceptional forecasting capabilities compared to other neural network architectures. To tackle the fuzzy datasets, fuzzy LSTM (FLSTM) model was developed by incorporating the advantage of the intuitionistic fuzzy logic (IFL). Most of the time series data generated from different fields including agriculture are not only fuzzy, but also exhibit nonlinear and non-stationary characteristics. The present study proposed wavelet-based fuzzy LSTM (WaveFLSTM) model, a novel approach for forecasting complex time series data, specifically addressing the challenges posed by fuzzy, nonlinear, and non-stationary characteristics of time series. The proposed WaveFLSTM has advantage of denoising through maximal overlap discrete wavelet transform (MODWT) and integrating the advantage of fuzzy logic by means of IFL. The fuzzy relations with LSTM networks are applied to each of the denoised series by using membership and non-membership values through intuitionistic fuzzy c-means technique. The prediction accuracy of proposed WaveFLSTM model is compared with that of LSTM, FLSTM and wavelet LSTM (WaveLSTM) models using monthly wholesale price data of different pulse crops from various markets in India. The percentage gain in accuracy of the proposed model, as compared to LSTM, WaveLSTM, and FLSTM, is found out to be 29%, 20%, and 14% respectively. Besides, the usual accuracy measures, the model confidence sets and technique for order preference by similarity to ideal solution algorithm have also been used. The findings demonstrated the effectiveness of the proposed WaveFLSTM model in improving forecasting accuracy of complex time series data.