A Noise-Aware Weighted Fuzzy Rough Set Model for Feature Selection

Fuzzy rough set theory has made significant strides in the field of feature selection. However, it still faces challenges when dealing with noisy data. Most traditional models fail to incorporate sample weight information in the evaluation of sample similarity, leaving them prone to interference from noisy samples. To address this issue, this article introduces a novel Weighted Fuzzy Rough Set (WFRS) model, designed to more accurately capture the uncertainty inherent in data. This model combines class distribution with the concept of neighborhood weights for samples, and proposes a directed weighted fuzzy binary relation to evaluate both the similarity and differences between samples. By doing so, it avoids the overfitting issues typically caused by over-reliance on distribution information from local noisy samples. Drawing on sample weighting, traditional fuzzy approximation operators are reinterpreted and redefined, leading to the construction of the WFRS model. Key uncertainty metrics, such as decision approximation and the positive region, are analyzed in depth, providing a solid theoretical foundation for subsequent feature selection and decision analysis. Based on this model, a forward heuristic feature selection algorithm is developed and compared with various State-of-the-Art algorithms. Experimental results demonstrate that the proposed method performs exceptionally well across multiple evaluation metrics, fully validating the efficiency and robustness of the WFRS model.