Abstract: Attribute reduction is an important issue in rough set theory, since the decision information systems are often included incomplete data in practical applications. Therefore, the incomplete decision table is transferred into a set-valued decision information system, and then the distribution reduction and the maximum distribution reduction based on similar relation in the set-valued decision information system are analyzed. On this basis, an attribute reduction algorithm based on the distinguishable set of objects is proposed, which uses the distinguishable set of objects’ sets. All results of the distribution reduction and the maximum distribution reduction are calculated by the minimum disjunctive normal form. Finally, an illustrative example shows the feasibility of the algorithm.

Key words: rough sets, incomplete decision table, set-valued information system, distinguishable set of objects, distribution reduction, maximum distribution reduction

摘要： 属性约简是粗糙集理论中重要研究内容，由于现实应用领域中决策信息系统往往呈现出不完备性特点，为此，首先将不完备决策表转化为集值决策信息系统，并详细分析了集值决策信息系统下基于相似关系的分布约简和最大分布约简，在此基础上，构造了一种基于可区分对象集的属性约简算法，算法利用可区分对象集的集对，计算极小析取范式求解出所有的分布约简和最大分布约简。最后，利用实例分析验证了算法的有效性。

关键词: 粗糙集, 不完备决策表, 集值决策信息系统, 可区分对象集, 分布约简, 最大分布约简