Attribute Reduction Based on Weighted <i>k</i>-Nearest Neighborhood in Hybrid Decision Information System

属性约简是粗糙集理论的一项重要应用，大多数的邻域粗糙集模型只关注邻域粒完全包含在某些决策类中的对象，而忽略邻域粒不包含在任何决策类中的边界对象的可分性。本文采用k近邻来描述混合信息系统对象的粒化，利用边界对象邻域粒中对象的决策信息以及在各自决策类中的分布情况构造对象的评价函数，并基于此定义近似正域。进而在混合型信息系统上提出基于加权k近邻的约简定义，给出属性的重要性度量，以及基于加权k近邻的属性约简方法。最后在3个混合数据集上对约简结果的分类精度进行比较。与传统邻域粗糙集的属性约简算法相比，该算法能保证约简后数据有较高的分类精度。Attribute reduction is an important application of rough set theory. Most neighborhood rough set models only focus on the objects whose neighborhood granules are completely contained in some decision classes, but ignore the divisibility of boundary objects whose neighborhood granules are not contained in any decision classes. In this paper, the k-nearest neighborhood is used to describe the granulation of hybrid information system objects. The evaluation function of objects is constructed by using the decision information of objects in the neighborhood of boundary objects and their distribution in their decision classes. Then, the definition of reduction based on weighted k-nearest neighborhood is proposed in hybrid information system, the importance measure of attribute and the attribute reduction method based on weighted k-nearest neighborhood are given. Finally, the classification accuracy of the reduction results is compared on 3 mixed data sets. Compared with the traditional neighborhood rough set attribute reduction algorithm, the proposed algorithm in this paper can ensure the high classification accuracy of the reduced data.