类对称关系下的广义粗糙集模型  

Generalized Rough Set Models Under Similar Symmetric Relations

作　　者：马周明[1] 李进金[1] 

机构地区：[1]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《计算机工程》2012年第5期70-72,82,共4页Computer Engineering

基　　金：国家自然科学基金资助项目(10971186;71140004;61170128);福建省属高校科研基金资助项目(JK2011031;JA11171)

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。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.

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 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]