A comparison of two types of rough approximations based on Nj-neighborhoods

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of N-j-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.