Abstract: Currently, data completion methods based on rough sets mostly compute the similarities between the object that contains missing values and other objects that do not contain missing values, and then use the values of the most similar object to complete the missing values. However, the problem in these methods is that all the condition attributes are considered as equally important, and they ignore the differences between condition attributes. Given this problem, a new notion of fuzzy weighted similarity is introduced, and the similarities between different objects are computed based on the dependencies of decision attribute on condition attributes and the significances of condition attributes. Moreover, the data completion method with rough sets based on the measurement of fuzzy weighted similarity is proposed. The validity of the proposed method is demonstrated by the results of comparative experiments.

Key words: rough sets, data completion, fuzzy weighted, similarity measure

摘要： 目前基于粗糙集的数据补齐方法，大多都是通过计算决策信息系统中具有缺失值的对象与无缺失值的对象之间的相似性，选取相似性最大的对象的属性值来补齐缺失的数据。这类算法的问题在于：计算对象之间的相似性时所有条件属性对于决策属性的重要性是相同的，忽略了条件属性间的差异性。鉴于此，引入了模糊加权相似的概念，根据每个条件属性的重要性以及决策属性对条件属性的依赖度，计算对象间的相似性，提出基于模糊加权相似性度量的粗糙集数据补齐方法，并通过实例计算以及与现有算法的比较分析，说明了方法的有效性。

关键词: 粗糙集, 数据补齐, 模糊加权, 相似性度量