Abstract: In order to get the maximum distribution attribute reduction rapidly in inconsistent decision information systems, a new decision maximum distribution binary relation was defined after analyzing the existing methods. And the judgment theorems for judging maximum distribution consistent sets were obtained, from which we can provide a new maximum distribution attribute reduction algorithm in inconsistent decision information systems. Moreover, the characterization of core attributes, relative necessary attributes, unnecessary attributes were discussed based on decision maximum distribution binary relation. Finally, a case study illustrates the validity of the method.

Key words: rough set, decision maximum distribution binary relation, attribute reduction, discernable matrix

摘要： 针对如何快速求解不协调决策信息系统的最大分布属性约简问题，在分析现有的约简方法的基础上，定义一种新的决策最大分布二元关系，得到了最大分布协调集的判定定理，建立起了一种不协调决策信息系统最大分布属性约简的新方法。并进一步分析了最大分布的核心属性、相对必要属性、不必要属性的相应的特征刻画。最后给出了一个实例验证本方法的有效性。

关键词: 粗糙集, 决策最大分布二元关系, 属性约简, 可辨识矩阵