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中文摘要：
上、下近似集是粗糙集理论中重要内容之一。使用矩阵理论来研究概率粗糙集上、下近似的计算，通过等价关系矩阵和子集的列矩阵之间的运算来得出上、下近似集；属性约简是粗糙集中规则提取的重要步骤，通过下近似列矩阵之间的运算来得出知识的相对正域，删除冗余属性，从而实现属性约简。
英文摘要：
The upper and lower approximations are one of the important topics in the research on rough set theory. The upper and lower approximation operators of probability rough set are redefined using the matrix operation between equivalent relation matrix and column matrix;the key step in the rules extraction of rough set is attribute reduction. The lower approximation matrix is computed to obtain the relative positive domain and delete redundant attributes, and gets attribute reduction.
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