不完备邻域粗糙集的不确定性度量和属性约简

针对现有的属性约简算法不适合处理数值型属性和符号型属性共同存在的不完备数据，提出了一种拓展不完备邻域粗糙集模型。首先，通过考虑属性值的概率分布来定义缺失属性值之间的距离，可以度量具有混合属性的不完备数据；其次，定义了邻域混合熵来评价属性约简的质量，分析证明了相关的性质定理，并构造了一种基于邻域混合熵的不完备邻域粗糙集属性约简算法；最后从UCI数据集中选取了7组数据进行实验，并分别与基于依赖度的属性约简（ARD）、基于邻域条件熵的属性约简（ARCE）、基于邻域组合测度的属性约简（ARNCM）算法进行了比较。理论分析和实验结果表明，所提算法约简属性比ARD、ARCE、ARNCM分别减少了约1，7，0个，所提算法的分类精度比ARD、ARCE、ARNCM分别提高了约2.5，2.1，0.8个百分点。所提算法不仅能够获得较少的约简属性，同时具有较高的分类精度。

Uncertainty measurement and attribute reduction in incomplete neighborhood rough set

Focusing on that the existing attribute reduction algorithms are not suitable for dealing with the incomplete data with both numerical attributes and symbolic attributes, an extented incomplete neighborhood rough set model was proposed. Firstly, the distance between the missing attribute values was defined to deal with incomplete data with mixed attributes by considering the probability distribution of the attribute values. Secondly, the concept of neighborhood mixed entropy was defined to evaluate the quality of attribute reduction and the relevant property theorem was proved. An attribute reduction algorithm for incomplete neighborhood rough set based on neighborhood mixed entropy was constructed. Finally, seven sets of data were selected from the UCI dataset for experimentation, and the algorithms was compared with the Attribute Reduction of Dependency (ARD), the Attribute Reduction of neighborhood Conditional Entropy (ARCE) and the Attribute Reduction of Neighborhood Combination Measure (ARNCM) algorithm respectively. The theoretical analysis and the experimental results show that compared to ARD, ARCE, ARNCM algorithms, the proposed algorithm reduces the attributes by about 1, 7, 0 respectively, and improves the classification accuracy by about 2.5 percentage points, 2.1 percentage points, 0.8 percentage points respectively. The proposed algorithm not only has less reducted attributes, but also has higher classification accuracy.