In this paper, we discuss the approximation operators [...] apr¯NS ${\overline{apr}}_{NS}$ and [...] apr¯S ${\overline{apr}}_S$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.