基于布尔差别矩阵逻辑运算的属性约简

针对差别矩阵属性约简存在的不足，首先将决策表简化，并引入布尔差别矩阵定义及其逻辑运算方法；然后给出基于布尔差别矩阵核属性和属性约简的定义，同时证明了该核属性和属性约简与正区域的核属性和属性约简是等价的；接着，设计基于属性布尔差别矩阵逻辑运算的属性约简算法，算法的时间和空间复杂度均为O(|C||U/C|2)。最后，通过实例和实验验证本文算法的正确性和高效性。

Attribute Reduction Based on Logical Operation of Boolean Discernibility Matrix

In order to solve the shortcomings of computing attribute reduction based on discernibility matrix, firstly, the decision tables is simplified, and the definition of bloolean discernibility matrix and the method of logical operation based on boolean discernibility matrix are provided. Secondly, the corresponding definitions of core attributes and attribute reduction based on boolean discernibility matrix are put forward. It is proved that core attributes and attribute reduction acquired from the definitions are equivalent to the core attributes and attribute reduction based on positive region. And then, the algorithm for computing attribute reduction based on logical operation of boolean discernibility matrix is designed, and its time and space complexity are all O(|C||U/C|2). Finally, the example and experiments are used to explain the feasibility and effectiveness of the method.