Rough set paradigms via containment neighborhoods and ideals

Abstract

Imperfect information causes indistinguishability of objects, and then unable to make 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 dierent standpoints like topology and ideal. In this manuscript,
we make use of the system of containment neighborhoods to present new rough set models generated
by topology and ideal. 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.