关键词: 不完备信息系统, 特征关系, 粗糙集, 知识约简

Abstract: The generalized incomplete system is deeply investigated in this paper.In such information system，“do not care” and lost unknown attribute values coexist.Based on the characteristic relation，the approach to knowledge reduction in the generalized information system is discussed.Moreover，the concepts of the lower and upper approximate distribution reductions are introduced into the generalized incomplete objective information system.The judgment theorems and discernibility formulas associated with these approximate distribution reductions are presented.Finally，an illustrative example is used to show the validity of the approaches to the lower and upper distribution reductions in the generalized objective information system.

Key words: incomplete information system, characteristic relation, rough set, knowledge reduction