Trend-pattern unlimited fuzzy information granule-based LSTM model for long-term time-series forecasting

Trend fuzzy information granulation has shown promising results in long-term time-series forecasting and has attracted increasing attention. In the forecasting model based on trend fuzzy information granulation, the representation of trend granules plays a crucial role. The research focuses on developing trend granules and trend granular time series to effectively represent trend information and improve forecasting performance. However, the existing trend fuzzy information granulation methods make assumptions about the trend pattern of granules (i.e., assuming that granules have linear trends or definite nonlinear trends). Fuzzy information granules with presupposed trend patterns have limited expressive ability and struggle to capture complex nonlinear trends and temporal dependencies, thus limiting their forecasting performance. To address this issue, this paper proposes a novel kind of trend fuzzy information granules, named Trend-Pattern Unlimited Fuzzy Information Granules (TPUFIGs), which are constructed by the recurrent autoencoder with automatic feature learning and nonlinear modeling capabilities. Compared with the existing trend fuzzy information granules, TPUFIGs can better characterize potential trend patterns and temporal dependencies, and exhibit stronger robustness. With the TPUFIGs and Long Short-Term Memory (LSTM) neural network, we design the TPUFIG-LSTM forecasting model, which can effectively alleviate error accumulation and improve forecasting capability. Experimental results on six heterogeneous time series datasets demonstrate the superior performance of the proposed model. By combining deep learning and granular computing, this fuzzy information granulation method characterizes intricate dynamic features in time series more effectively, thus providing a novel solution for long-term time series forecasting with improved forecasting accuracy and generalization capability.