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中文摘要：
利用拓扑学中内部这个重要的概念来刻画协调决策信息系统的属性约简与不协调决策信息系统关于下近似的约简，使拓扑与粗糙集两个理论交叉、渗透，在此基础上从拓扑的角度出发，更进一步地给出一个二元关系相对于一族二元关系的内部约简的概念，并且定义一个辨识矩阵来给出内部协调集的判定定理与内部约简的算法。最后，在覆盖广义粗糙集理论中认识这类约简，并给出一个应用模型。
英文摘要：
By employing an important concept, interior, in topology and intercrossing the theories of topology and rough sets, the attribute reduction in consistent information systems and lower approximation reduction in inconsistent information systems are recognized. Then, based on the theory of topology, the definition of in- terior reduction in a family of general relations is introduced, and a discernibility matrix is defined to present a judgement theorem for calculating interior consistent sets. Furthermore, a kind of reduction in covering generalized rough set theory is the same as the interior reduction and a model of its application is given.
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