Abstract: For consistent decision table, the attribute reductions based on relative granularity, relative partition granularity, knowledge quantity and common discernibility degree are equivalent with the algebraic reduction respectively. But they are inconsistent while the decision table is inconsistent. For inconsistent decision table, it is proved that the relationship between new conditional information entropy, knowledge quantity, common discernibility degree and relative granularity is linear. It is followed that the attribute reductions based on relative granularity, relative partition granularity, knowledge quantity and common discernibility degree are just equivalent with the one based on HU’s discernibility matrix. An inconsistent decision table is designed to illustrate the correctness of conclusion.

Key words: discernibility matrix, HU’s attribute reduction, conditional information entropy, relative granularity, knowledge quantity, common discernibility degree

摘要： 对于一致决策表，现有基于相对粒度、相对划分粒度、知识量和同可区分度的属性约简与分别代数约简是等价的，但对于不一致决策表，它们与代数约简并不等价。为此，针对不一致决策表，建立相对粒度与新条件信息熵、知识量和同可区分度之间的线性关系，从而得出结论：现有基于相对粒度、相对划分粒度、知识量和同可区分度的属性约简本质上仅与基于差别矩阵的HU属性约简等价，并通过设计一个不一致决策表验证该结论的正确性。

关键词: 差别矩阵, HU属性约简, 条件信息熵, 相对粒度, 知识量, 同可区分度

CLC Number: 

• TP18