(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

中文翻译：

---

一个新的单值中智粗糙集和相关拓扑

（模糊）粗糙集与（模糊）拓扑密切相关。中智粗糙集和中智拓扑分别是（模糊）粗糙集和（模糊）拓扑的扩展。本文提出了一种新型的中智粗糙集，讨论了它的基本性质和与中智拓扑的关系。主要结果包括： (1) 对于单值中智近似空间, 定义了一对近似算子，称为上、下普通单值中智近似算子，并讨论了它们的性质。然后探索了与自反（传递）单值中智近似空间相对应的所提出的近似算子的进一步性质。(2) 验证了单值中智近似空间和普通单值中智拓扑空间可以通过我们定义的下近似算子相互关联。特别地，自反、传递单值中智近似空间与拟离散普通单值中智拓扑空间之间存在一一对应的关系。