Axiomatic systems for rough set-valued homomorphisms of associative rings

Axiomatic approaches to study approximation operators are one of the primary directions for the investigation of rough set theory. In this paper, we provide some axiomatic systems of lower and upper approximation operators in rough set theory. We also apply the axiomatic systems of generalized rough sets for definitions of generalized lower and upper approximations with respect to an ideal of a ring and discuss some of their significant properties.