Idealization of j-approximation spaces

Abstract

The current work concentrates on generating dierent topologies by using ideals. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was rst proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of rough set theory is reducing
the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned reasoning, we propose in this paper three dierent methods based on ideals to achieve this aim.
Many interesting properties of this type of generalized rough sets are derived. These methods are more accurate of the previous methods and hence it is very interesting in rough set context for removing the vagueness (uncertainty).