变精度极大相容块粗糙集模型及其属性约简

Maximum Consistent Block Based Variable Precision Rough Set Model and Attribute Reduction

主要研究不完备信息系统的属性约简问题。首先基于极大相容块构造乐观和悲观两种广义变精度粗糙集模型,分析两种模型之间的关系并研究其主要性质。在此基础上,定义乐观(悲观)β-下分布约简和β-上分布约简并且给出相应的判定定理,进而得到一种保持决策类上(下)近似分布不变的属性约简方法--布尔计算方法。这种构造极大相容块间的辨识矩阵的方法缩小了矩阵的规模,进而简化了计算属性约简的过程,从而能够有效地节省计算时间和存储空间。然后对含有"丢失""不关心"值和只有"不关心"值的两种不完备信息系统进行实例分析,最后从UCI数据集中选取5组不完备信息数据集来验证方法的有效性。

In this paper, attribute reduction of incomplete information system is studied. Firstly, optimistic and pessimistic generalized variable precision rough set models based on maximal consistent blocks are constructed.The relationship between the two models and their main properties are analyzed. After that β-lower optimistic(pessimistic) and β-upper distribution attribute reduction is defined, and the corresponding judgement theorem is given. Boolean method of attribute reduction is obtained, and it can keep the upper(lower) approximation distribution of the decision class unchanged. This method of constructing discernibility set between maximal consistent blocks reduces the size of the discernibility matrix, and the process of computing attribute reduction is simplified, which can effectively save computing time and storage space. Then two examples of incomplete information systems with"lost""dont care"values and only"dont care"values are employed to illustrate the proposed method. Finally, 5 sets of incomplete information data sets from UCI data set are used to validate its effectiveness.