Imperfect information causes indistinguishability of objects and inability of making an accurate decision. To deal with this type of vague problem, Pawlak proposed the concept of rough set. Then, this concept has been studied from different points of view like topology and ideals. In this manuscript, we use the system of containment neighborhoods to present new rough set models generated by topology and ideals. We discuss their fundamental characterizations and reveal the relationships among them. Also, we prove that the current approximation spaces produce higher accuracy measures than those given by some previous approximation spaces. Ultimately, we provide a medical example to demonstrate that the current approach is one of the preferable and useful techniques to eliminate the ambiguity of the data in practical problems.