Abstract: Combining the discernibility matrix and the recently proposed fast algorithm, this paper studies the reduction algorithm for relational system and the distributed reduction algorithm for relational decision system. Research shows that the distributed reduction of the relational decision system is actually the reduction of the relation system when the decision attribute is self-reflexive. Additionally, interval-valued fuzzy ordered relational decision system is as a special case of the relational decision system, whose all reduction results can be obtained through the distributed reduction algorithm for relational decision system which simplifies the original reduction algorithm.

Key words: attribute reduction, relation decision system, distribution reduction, discernibility matrix, interval value

摘要： 基于分辨矩阵和最近已提出的快速算法，对关系系统的约简算法和关系决策系统的分布约简算法进行了研究。证明当决策属性具有自反性时，关系决策系统的分布约简实际上就是关系系统的约简，与决策属性无关。此外，区间值模糊序关系决策系统可视为关系决策系统的一个特例，用提出的关系决策系统的分布约简算法即可获得区间值模糊序关系决策系统的全部约简结果，从而简化了原来的约简算法。

关键词: 属性约简, 关系决策系统, 分布约简, 分辨矩阵, 区间值