摘要
文献[1]中的相对闭包不能对应于覆盖广义粗集理论中的另一个主要概念覆盖上近似集。因此本文给出了关于子基β的相对闭包的另一种定义,使之能对应于覆盖广义粗集理论中的覆盖上近似集。主要结果:相对闭包的一些基本性质、同一拓扑的两个子基会生成相同的相对闭包运算的充分必要条件、相对内部运算和相对闭包运算的相互依赖性。这些结果可以看作是覆盖广义粗集的理论基础。
Relative closure operators in Topological Methods on the Theory of Covering Generalized Rough Sets don＇t correspond to the upper approximation operators. So in this paper another relative closure operator in a topological space is defined, which corresponds to the upper approximation operator in the theory of covering generalized tough sets. It obtains three results-properties of relative closures in a topological space , necessary and sufficient conditions for relative closure operators, generated by two subbases of the same one topology, to be the same, respectively, the mutual dependance of relative interior and relative closure. These results can be considered as fundamental theory of covering generalized rough sets.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2005年第6期675-678,共4页
Pattern Recognition and Artificial Intelligence
基金
国家自然科学基金(No.10271056
10571151)
福建省自然科学基金(No.Z051133)
关键词
拓扑
粗集
覆盖上近似集
相对闭包
Topology, Rough Set, The Covering Upper Approximation Set, The Relative Closure
