Abstract: The incomplete decision table in which lost and “do not care” unknown values are coexisting is thoroughly investigated．Based on a new dual relation，approach to knowledge reduction and extraction rules in the incomplete decision table is studied． From the view point of new dual relation based rough set model，the knowledge reduction is introduced into the incomplete decision system． The judgment theorems and discernibility matrixes associated with these knowledge reductions are also obtained． The research is meaningful both in the theory and in applications for the acquisition of rules in the complex incomplete decision system.

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

摘要： 以同时具有丢失型和遗漏型未知属性值的不完备系统为研究对象，提出了一种新的二元关系并基于此关系讨论了其中的知识约简和规则提取问题。在不完备决策系统中，引入了约简、区分矩阵、广义区分矩阵等概念并给出了约简的判定定理和算法，为从复杂的不完备决策系统中获取知识提供了新的理论基础与技术手段。

关键词: 不完备信息系统, 特征关系, 粗糙集, 知识约简