中文摘要：

粗糙集理论是一种处理不确定性知识的有效工具，属性约简是其核心内容之一，然而对于属性值有缺省的不完备信息系统，基于等价关系的经典粗糙集理论已经不再适用。由于容差关系下的不完备信息系统的属性约简的定义与经典粗糙集的属性约简定义相似，可以用容差关系对粗糙集理论进行扩充。文中通过定义容差关系下的可辨识矩阵，运用可辨识方法，得到了一种属性约简算法；接着分析了算法的不足之处，并且在此基础上提出了增加约简效率的改进型算法；最后通过一个数值例子，说明了该算法是合理的和有效的。

英文摘要：

Rough set theory is a kind of effective tool for dealing with uncertainty knowledge. Attribute reduction is one of the most im- portant content. Nevertheless, the classical rough set theory based on equivalence relation has not been applied for the incomplete informa- tion system which some attribute is the default value. The definition that attributes reduction of incomplete information system is similar to the classical rough set because of the tolerance relation. Can expand the classical rough set theory with tolerance relation. In this paper,by defining the discernibility matrix under the tolerance relation, obtain an attribute reduction algorithm through discernibility method. Then analyze the deficiency of the algorithm and put forward a kind of modified algorithm that can improve efficiency of the reduction. At last, prove the reasonableness and validity of the algorithm through a numerical example.