基于扩展容差关系的不完备信息系统属性约简

针对当前的邻域粗糙集多用于处理完备的信息系统，而非不完备的信息系统这一问题，提出了一种可用于处理不完备混合信息系统的扩展容差关系，并给出相关定义，使用容差完备度和邻域阈值作为限制条件计算扩展容差邻域，以此邻域为基础选择决策正域得到系统的属性重要性，并以该重要性作为启发因子给出基于扩展容差关系的属性约简算法。采用UCI数据集中的7组不同类型的数据集进行仿真实验，并分别与扩展邻域关系（EN）、容差邻域熵（TRE）、邻域粗糙集（NR）的方法进行比较，实验结果表明，该方法在保证分类精度的同时能够约简得到更少的属性。最后讨论了在扩展容差关系中改变邻域阈值对分类精度产生的影响。

Attribute reduction in incomplete information systems based on extended tolerance relation

Current neighborhood rough sets have been usually used to solve complete information system, not incomplete system. In order to solve this problem, an extended tolerance relation was proposed to deal with the incomplete mixed information system, and associative definitions were provided. The degree of complete tolerance and neighborhood threshold were used as the constraint conditions to find the extended tolerance neighborhood. The attribute importance of the system was got by the decision positive region within the neiborhood, and the attribute reduction algorithm based on the extended tolerance relation was proposed, which was given by the importance as the heuristic factor. Seven different types of data sets on UCI database was used for simulation, and the proposed method was compared with Extension Neighborhood relation (EN), Tolerance Neighborhood Entropy (TRE) and Neighborhood Rough set (NR) respectively. The experimental results show that, the proposed algorithm can ensure accuracy of classification, select less attributes by reduction. Finally, the influence of neighborhood threshold in extended tolerance relation on classification accuracy was discussed.