Abstract: The distribution reduction and maximum distribution reduction in inconsistent decision table based on dominance relations is studied.This paper points out that the results about the distribution reduction and maximum distribution reduction in reference[9] is not correct.Firstly，by giving a counterexample，the paper points out errors of the judgment theorems of the distribution reduction and maximum distribution reduction in reference[9]，and the cause of these mistakes is analyzed.Secondly，this paper points out the methods based on discernibility matrix for calculating the distribution reduction and maximum distribution reduction in reference[9] is not correct.Therefor，the concept of absolute reduction in inconsistent decision table based on dominance relations is introduced，and it is proved that the absolute reduction is equal to the distribution reduction and maximum distribution reduction.Furthermore，a new maximum distribution reduction is discussed and proved that the new maximum distribution reduction is equal to the lower approximation reduction.

Key words: rough set, decision table, distribution reduction, maximum distribution reduction, absolute reduction, lower approximation reduction

摘要： 研究了优势关系下不协调决策表的分布约简和最大分布约简问题，指出文献[9]关于分布约简和最大分布约简的几个结论是错误的。首先用反例指出文献[9]给出的分布约简和最大分布约简的判定定理是错误的，分析了错误的原因。其次，利用这些定理所得到的辨识矩阵，用来求分布约简和最大分布约简也是错误的。为此，引入了优势关系下不协调决策表的绝对约简的概念，证明了绝对约简与分布约简和最大分布约简是等价的。另外，讨论了另一种新的最大分布约简，并证明新的最大分布约简与下近似约简是等价的。

关键词: 粗糙集, 决策表, 分布约简, 最大分布约简, 绝对约简, 下近似约简