摘要： 针对等价关系下的经典粗糙集，定义弱对称与局部强对称二元关系，构造相应的广义粗糙集模型。给出这2种模型的公理化特征，并将两者结合，得到强对称二元关系下的广义粗糙集模型。理论分析证明，论域上任何集合均为广义精确集的充要条件是其二元关系为强对称关系，即可以利用该模型刻画经典粗糙集中的广义精确集。

关键词: 经典粗糙集, 广义粗糙集, 等价关系, 强对称关系, 公理化特征, 广义精确集

Abstract: According to the classical rough sets based on the equivalences, this paper presents the weak symmetric and partial strong symmetric binary relations, establishes the generalization rough set models based on the two relations. It gives the axiomatic characterizations of the two models. Combining both of the two models, it gets the generalized rough set model based on strong symmetric relation. Results of theoretical analysis demonstrate that a necessary and sufficient condition for that all sets of the universe are the generalized accurate sets is the binary relation on universe is a strong symmetric relation, namely, the model can be used to put up a characterization of the generalized accurate set in the classical rough sets.

Key words: classical rough set, generalized rough set, equivalence relation, strong symmetric relation, axiomatic characterizations, generalized accurate set

中图分类号: 

• TP311