Abstract: Attribute reduction of an information system with real value attributes is one of the research hot spots in rough set theory. Instead of an equivalence relation with discretization of real values, a kind of similarity relation and its adaptive form based on fuzzy c-means clustering are proposed. A rough set model based on the similarity relation is presented which has good performance in dealing with noisy data. A kind of importance degree derives from the defined positive region and nonpositive one, the attribute reduction of an information system is performed. Comparative experiments with existing method show that the proposed method is effective, stable and reasonable.

Key words: rough set, attribute reduction, fuzzy c-means, similarity relation

摘要： 对具有连续属性值的信息系统的属性约简是粗糙集理论的研究热点之一。区别于传统通过连续属性离散化方法定义的等价关系，提出利用自适应的模糊C均值聚类的初步划分能力定义一种相似关系以及其自适应形式。基于该相似关系定义的粗糙集模型较好地排除噪声数据。提出正域与非正域定义以及从中导出的一种重要度以指导属性约简。与现有方法的比较实验表明该方法在属性约简上具有有效性和稳定性以及约简结果的合理性。

关键词: 粗糙集, 属性约简, 模糊C均值, 相似关系