中文摘要：

将变精度粗糙集模型引入模糊目标信息系统,建立了模糊目标信息系统的变精度粗糙集模型。定义了四种该模型上的知识约简——β上下近似约简和β上下分布约简;讨论了β上下分布约简的一些性质,提出了β上下分布协调集的判定定理,通过定义相应的区分矩阵给出了求β上下分布约简的区分矩阵算法。

英文摘要：

Knowledge reduction is one of the most important tasks in rough set theory. A variable precision rough set model upper and lower theorem and the means of which, is introduced into fuzzy objective information systems, on which four knowledge reductions,β approximation reduction, β upper and lower distribution reduction are defined. The iudgment discernibility matrix with respect toβ upper and lower distribution consistent set is obtained, by the method of β upper and lower distribution reduction is presented.