Fuzzy rough set (FRS) theory is generally used to measure the uncertainty of data. However, this theory cannot work well when the class density of a data distribution differs greatly. In this work, a relative distance measure is first proposed to fit the mentioned data distribution. Based on the measure, a relative FRS model is introduced to remedy the mentioned imperfection of classical FRSs. Then, the positive region, negative region, and boundary region are defined to measure the uncertainty of data with the relative FRSs. Besides, a relative fuzzy dependency is defined to evaluate the importance of features to decision. With the proposed feature evaluation, we propose a feature selection algorithm and design a classifier based on the maximal positive region. The classification principle is that an unlabeled sample will be classified into the class corresponding to the maximal degree of the positive region. Experimental results show the relative fuzzy dependency is an effective and efficient measure for evaluating features, and the proposed feature selection algorithm presents better performance than some classical algorithms. Besides, it also shows the proposed classifier can achieve slightly better performance than the KNN classifier, which demonstrates that the maximal positive region-based classifier is effective and feasible.

中文翻译：

---

特征选择和分类的相对模糊粗略近似


模糊粗糙集（FRS）理论通常用于衡量数据的不确定性。然而，当数据分布的类密度差异很大时，该理论就不能很好地发挥作用。在这项工作中，首先提出了相对距离度量来拟合上述数据分布。在此基础上，引入了相对FRS模型来弥补经典FRS的缺陷。然后，定义正区域、负区域和边界区域，用相对FRS来衡量数据的不确定性。此外，还定义了相对模糊依赖性来评估特征对决策的重要性。根据所提出的特征评估，我们提出了一种特征选择算法，并设计了一个基于最大正区域的分类器。分类原则是，将未标记的样本分类到正区域最大程度对应的类中。实验结果表明，相对模糊依赖是一种有效且高效的特征评估指标，所提出的特征选择算法比一些经典算法具有更好的性能。此外，它还表明所提出的分类器可以取得比KNN分类器稍好的性能，这表明基于最大正区域的分类器是有效和可行的。