In long-term forecasting, the conversion of raw time series into granular time series (GTS) is generally regarded as an effective approach to reduce error accumulation. However, GTS still faces challenges, including insufficient feature extraction and excessive redundant information. To address these issues, this paper proposes a long short-term memory network (LSTM) prediction model that incorporates three-way decision (3WD) and quadratic fuzzy information granules (QFIGs) for long-term time series forecasting. An adaptive threshold is applied to the \(L_1\) -trend filtering to obtain a data-driven segmentation of the time series. QFIGs are then employed to construct the GTS to capture nonlinear local trends. Subsequently, a conditional probability and a loss function based on the similarity between QFIGs are defined, followed by the application of a 3WD-based granule aggregation rule. Finally, multiple LSTMs are used to predict the features of QFIGs over long horizons, aiming to improve prediction accuracy and efficiency. Compared with conventional GTS models, the proposed approach is designed to capture nonlinear trends, mitigate error accumulation, and preserve key features while reducing the impact of redundant information, with the goal of extending the applicability of 3WD in time series forecasting. Experimental results on several datasets suggest that the proposed model achieves competitive performance compared to classical and granular-based forecasting methods across multiple prediction horizons.
