title: Topology theory on rough sets.
abstract: For further studying the theories and applications of rough sets (RS), this paper proposes a new theory on RS, which mainly includes topological space, topological properties, homeomorphism, and its properties on RS by some new definitions and theorems given. The relationship between partition and countable open covering is discussed, and some applications based on the topological rough space and its topological properties are introduced. Moreover, some perspectives for future research are given. Throughout this paper, the advancements of the new theory on RS and topological algebra not only represent an important theoretical value but also exhibit significant applications of RS and topology.
authors.affiliation: School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China. wqe969699@163.com
authors.forename: QingE
authors.initials: Q
authors.lastname: Wu
authors.forename: Tuo
authors.initials: T
authors.lastname: Wang
authors.forename: YongXuan
authors.initials: Y
authors.lastname: Huang
authors.forename: JiSheng
authors.initials: J
authors.lastname: Li
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted