S²FS: Spatially-Aware Separability-Driven Feature Selection in Fuzzy Decision Systems

Feature selection is crucial for fuzzy decision systems (FDSs), as it identifies informative features and eliminates rule redundancy, thereby enhancing predictive performance and interpretability. Most existing methods either fail to directly align evaluation criteria with learning performance or rely solely on nondirectional Euclidean distances to capture relationships among decision classes, which limits their ability to clarify decision boundaries. However, the spatial distribution of instances has a potential impact on the clarity of such boundaries. Motivated by this, we propose spatially-aware separability-driven feature selection (S²FS), a novel framework for FDSs guided by a spatially-aware separability criterion. This criterion jointly considers within-class compactness and between-class separation by integrating scalar-distances with spatial directional information, providing a more comprehensive characterization of class structures. S²FS employs a forward greedy strategy to iteratively select the most discriminative features. Extensive experiments on 11 real-world datasets demonstrate that S²FS consistently outperforms ten state-of-the-art feature selection algorithms in both classification accuracy and clustering performance, while feature visualizations further confirm the interpretability of the selected features.