关于粗糙集中的导集拓扑及性质之研究

Study on the Guide Set Topology and Its Properties of Rough Sets

为了研究粗糙集与导集拓扑之间的关系,文中以粗糙集、导集运算、拓扑空间为研究对象,采用文献研究法、数学方法、探索性研究法,先定义了粗糙集中的导集运算,然后构建和证明了糙集中的导集拓扑,研究结果表明糙集中的存在导集拓扑,并取得了在粗糙集中用开集公理建立的拓扑和用导集运算建立的拓扑是等价的、粗糙集中满足导集运算和拓扑空间闭包运算的结论,该结论推广了粗糙集中已有的拓扑研究。

In order to study the relationship between rough sets and guide set topologies,this thesis takes rough set theory,guides set operations,and topological space as research objects,using literature research method,mathematical method and exploratory research method.First,this paper defines the guide set operation in rough set,and then constructs and proves the rough set topological topology,the results show that there is existence of guide set topology in rough set,and reaches the conclusions that the topology established by the open set axioms in the rough set is equivalent to the topology established by the guide set operations,rough set satisfies the guide set operation and topological space closure operation,the conclusion promotes the study of the existing research on topology of rough set.