一种基于加权相似性的粗糙集数据补齐方法

近年来，对不完备数据的处理引起了人们的广泛关注。目前，在粗糙集理论中已经提出了多种不完备数据补齐方法，这些方法通常需要计算决策表中具有缺失值的对象与其他没有缺失值的对象之间的相似性，并以最相似对象的取值来代替缺失值。然而，这些方法普遍存在一个问题，即在计算决策表中对象之间的相似性时假设决策属性对所有条件属性的依赖性都是相等的，而且所有条件属性都是同等重要的，并没有考虑不同条件属性之间的差异性。针对这一问题，引入一个加权相似性的概念，以决策属性对条件属性的依赖性和条件属性的重要性作为权值来计算相似性。基于加权相似性，提出一种新的粗糙集数据补齐算法WSDCA。最后，在UCI数据集上，将WSDCA算法与现有的数据补齐算法进行了比较分析。实验结果表明，所提出的数据补齐方法是有效的。

Rough Set Approach to Data Completion Based on Weighted Similarity

In recent years,much attention has been given to the treatment of incomplete data. By now,many completion methods to incomplete data have been proposed in rough set theory. hhese methods usually compute the similarities between the object that contains missing values and other objects that do not contain missing values,and use the values of the most similar object to replace the missing values. However, there is a common problem for these methods. That is,these methods assume that the dependencies of decision attribute on all condition attributes arc the same, and the significances of all condition attributes are also the same,they ignore the differences between different condition attributes in a decision table. To solve this problem, in this paper we introduced a new notion of weighted similarity, which employs the dependencies of decision attribute on condition attributes and the significances of condition attributes as weights to compute the similarity. Based on the weighted similarity, we proposed a novel rough set data completion algorithm WSDCA.We compared WSDCA with the current data completion algorithms on UCI data sets. And experimental results demonstrate the effectiveness of our method to data completion.