Heterogeneous Trend Fuzzy Information Granule-Based FCM-Transformer for Long-Term Forecasting

Long-term forecasting based on trend fuzzy information granulation has been extensively developed in machine learning and artificial intelligence. However, existing studies predominantly focus on the representation and modeling of single-type data, while research on heterogeneous time series that simultaneously contain real, interval, and nominal variables remains relatively scarce. To address this gap, this article introduces a novel granular structure, termed the heterogeneous trend fuzzy information granule (HTFIG), which uniformly encapsulates the trend information and the inherent heterogeneity of disparate variable types within such series. To mitigate over-segmentation in the initial granulation outcomes, we further devise a dynamic programming-based optimization strategy. This approach adaptively merges adjacent and similar granules by minimizing a trend mismatch score, thereby enhancing the compactness of the granular representation. Building on this foundation, we construct an HTFIG-based fuzzy cognitive map-Transformer forecasting framework. This framework synergistically integrates the causal reasoning capacity of fuzzy cognitive maps with the long-range dependency modeling power of the Transformer architecture, thereby enabling high-precision and interpretable long-term forecasting. To the best of our knowledge, this study constitutes the first systematic effort to introduce trend granulation modeling to the heterogeneous time-series context. Experimental results demonstrate that our proposed model consistently outperforms state-of-the-art benchmarks in both forecasting accuracy and interpretability, confirming its efficacy and superiority.