三类正负域覆盖粗糙集模型及其算子公理化
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摘要
覆盖广义粗糙集是经典粗糙集的一种理论和应用上有意义的推广。针对覆盖广义粗集边界过于粗糙及运算公理化定义难以得到的不足,首先,基于正、负域的定义,给出了三类正负域覆盖粗糙集模型的定义。其次,研究了这三类正负域覆盖粗糙集的一些基本性质。最后,从负域算子的角度,分别给出了这三类正负域覆盖粗糙集的公理化系统,并验证了它们之间的独立性。
Covering generalized rough sets is a meaningful extension for classical rough sets. As for the vagueness of covering generalized boundary and its incomplete axiomatic systems,based on the definition of positive-negative region,this paper defines three types of positive-negative region covering rough sets,investigating some basic properties of each type of positive-negative region covering approximation operators,establishing the axiomatic systems of these three types of negative covering approximation operators based on the properties of their negative regions,and figuring out the axiomatic system of three types of positive – negative region covering rough sets,as well as proving the independence among them.
Covering generalized rough sets is a meaningful extension for classical rough sets. As for the vagueness of covering generalized boundary and its incomplete axiomatic systems,based on the definition of positive-negative region,this paper defines three types of positive-negative region covering rough sets,investigating some basic properties of each type of positive-negative region covering approximation operators,establishing the axiomatic systems of these three types of negative covering approximation operators based on the properties of their negative regions,and figuring out the axiomatic system of three types of positive – negative region covering rough sets,as well as proving the independence among them.
引文
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[7]Zhu F,Wang F Y.Reduction and axiomization of covering generalized rough sets[J].Information Sciences,2003,152(1):217-230.
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[2]Slowinski R.Intelligent decision support-Handbook of applications and advances of the rough sets theory[M].Boston:Kluwer Academic Publishers,1992:331-362.
[3]Leung Y,Wu W Z,Zhang W X.Knowledge acquisition in incomplete information systems:a rough set approach[J].European Journal of Operational Research,2006,168(1):164~180.
[4]Skowron A.Extracting laws from decision tables:a rough set approach[J].Computational Intelligence,1995,1l(2):371-388.
[5]Wang G Y,Hu J.Attribute reduction using extension of covering approximation space[J].Fundamenta Informaticae,2012,115(2):219~232.
[6]Wang G Y.Computing approach of core-valued attribute in decision table[J].Chinese Journal of Computers,2003,26(5):611-615.
[7]Zhu F,Wang F Y.Reduction and axiomization of covering generalized rough sets[J].Information Sciences,2003,152(1):217-230.
[8]Zhu F,Wang F Y.On the three types of covering rough sets[J].IEEE Transactions on Knowledge and Data Engineering,2007,19(8):1131-1144.
[9]Wang S P,Zhu F,Zhu P Y.Abstract inter dependency in rough sets[J].Journal of Nanjing University:Natural Sciences,2010,46(5):507-510.
[10]Bonikowski Z,Bryniarski E,Wybraniec U.Extensions and intentions in the rough set theory[J].Information Science,1998,107:149-167.