Abstract: The fuzzy rough set model incorporating relative distance was able to effectively improve the performance of attribute reduction under imbalanced data distributions. However, the determination of relative distance depended on the ratio of absolute distance to a data distribution measure, and the membership degree of a sample to a target decision class was characterized only by its separability from that specific class. This computational strategy limited the discriminability of samples with respect to a given class and affected the accuracy and efficiency of reduction. Therefore, a attribute reduction method integrating weights and relative fuzzy approximation was proposed. First, a weight function was defined to map the relative distance between samples and the target decision class, and a more effective weighted fuzzy approximation operator was constructed accordingly. Then, the rationality of the weighted relative fuzzy approximation was discussed based on sample discriminability. Finally, an attribute reduction algorithm of Weighted Relative K-order Fuzzy approximation based on the fuzzy rough dependency function (WRKF) was proposed. Experimental results show that the algorithm can effectively eliminate redundant attributes. Compared with the Relative Fuzzy Rough Approximations for attribute reduction (RFRA) algorithm, it achieves average classification accuracy improvements of 1.21 percentage points and 1.09 percentage points, and under 10% and 20% label noise, the average classification accuracy improvements are 1.59 percentage points and 2.48 percentage points, respectively. These results indicate that the algorithm not only ensures reduction effectiveness but also effectively enhances the classification performance and robustness of the reduction results. 

Key words:  fuzzy rough set, attribute reduction, weighting function, relative distance, sample discriminability

摘要： 结合相对距离的模糊粗糙集模型能够有效提升数据分布不平衡时的属性约简表现。然而，相对距离的确定依赖于绝对距离与数据分布测度的比值，且样本对目标决策类的隶属程度仅通过它与特定类的分离程度表征，这种计算策略限制了不同样本对给定类别的可判别性，从而影响了属性约简的准确性和效率。基于上述问题，本文提出一种融合权重与相对模糊近似的属性约简方法。首先，通过定义权重函数映射样本与目标决策类之间的相对距离，以构造更有效的加权相对模糊近似算子，并进一步提出加权相对 阶模糊粗糙集模型；其次，利用样本判别讨论加权相对模糊近似的合理性；最后，基于模糊粗糙依赖函数提出加权相对 阶模糊近似的属性约简算法（WRKF）。实验结果表明，该算法能有效剔除冗余属性，与RFRA(Relative Fuzzy Rough Approximations for attribute reduction)算法相比，分类精度平均提升了1.21和1.09个百分点，在引入10%和20%标签噪声的情况下，分类精度平均提升了1.59和2.48个百分点，这表明，该算法在保证约简效果的同时，能有效提升约简结果的分类性能以及鲁棒性。

关键词: 模糊粗糙集, 属性约简, 加权函数, 相对距离, 样本判别