The lower and upper approximations and homomorphisms between lower approximations in quotient groups
Waqas Mahmood, Waqas Nazeer, Shin Min Kang · Journal of Intelligent & Fuzzy Systems · 2017
Rough sets are an emerging mathematical tool in the field of data analysis. The relation between rough sets and algebraic systems (groups, rings and modules etc.) has already been identified. In this paper we studied the lower and upper approximations of a rough set in a quotient group. It can be proved that under certain assumptions the lower approximation is a normal subgroup of the quotient group; however this result is not valid for the upper approximation. We developed several homomorphisms between two lower approximations of the quotient groups.