三类正负域覆盖粗糙集模型及其算子公理化

Three Types of Positive-Negative Region Covering Rough Sets and Their Axiomation

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 cover- ing 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.