Topologies and approximation operators induced by binary relations

Abstract

Theory of rough sets is an extension of classic set theory, which is an important mathematical tool for dealing with uncertain or vague information. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. Topologies via relations have very important role in rough set theory. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood operators. Moreover, the relations among them are studied. In addition, lower and upper approximations of rough sets using the binary relation with respect to neighborhood operators are studied and examples are given.