摘要
为探索将拓扑学中的局部强连通性理论引入到粗糙集理论研究中,将Pawlak粗糙集导出拓扑空间作为研究对象,采用拓扑和范畴论方法来实验研究Pawlak粗糙集导出拓扑空间一些特征,实验结果表明粗糙集导出拓扑空间同样具有局部强连通性,并得出粗糙集导出拓扑空间有一个由具有强连通性开集组成的,并生成集具有等价性、开遗传性和连续不变性、直和性、导出的局部强连通拓扑空间,及其间的连续映射构成的范畴是拓扑结构的重要结论,合理推广了粗糙集的拓扑结构理论研究。
In order to explore the application of local strong connectivity theory in topology to the study of rough set theory,in this thesis,the topological space which was derived from the Pawlak rough set as the object of study,the topology and category theory were adopted to study some features of topological space derived from Pawlak rough sets. The experimental results show that the topological space derived from rough sets had the same local strong connectivity; some important conclusions were made that the rough set derived topological space had a strong connectivity,and open composition of the generating set was equivalent,genetic continuity and invariance,straight,and locally strongly connected topological spaces and continuous maps of the category were topological structure. These conclusions rationally promote theoretical research on Topological construct of rough sets.
作者
钟满田
ZHONG Man-tian(Department of Education,Luoding Polytechnic,Luoding Guangdong 527200,China)
出处
《安徽理工大学学报（自然科学版）》
CAS
2018年第1期78-81,共4页
Journal of Anhui University of Science and Technology:Natural Science
关键词
粗糙集模型
拓扑空间
局部强连通性
rough set model
topological space
local strong connectedness
