Abstract: The relationship between the attribute set of decision table, Boolean matrix and resolve of logic equation set is set up. And then the Boolean matrix representation of rough set theory in decision table based on the relationship is given. Finally, the equivalence properties between Boolean matrix representation and algebra representation of attribute reduction are proved. These conclusions are helpful for people to understand the essential of rough set theory and to build foundation for seeking new efficient algorithm of attribute reduction.

Key words: Rough set, Attribute reduction, Decision table, Boolean matrix

摘要： 建立了布尔矩阵与逻辑方程组的解和决策表中的属性集之间的关系；然后在此基础上给出了决策表中的粗糙集理论的布尔矩阵表示；最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。这些结论有助于人们深刻理解粗糙集理论的本质，同时为寻找高效的属性约简算法奠定了基础

关键词: 粗糙集, 属性约简, 决策表, 布尔矩阵