Near-Generalized Approximations in Groups Based on a Set-Valued Mapping

A normal subgroup of a group can partition a group into equivalence classes.Therefore, approximations can be constructed within a group.The near approximations in a group are extensions of the approximations in a group.A set-valued mapping T from group G to the set of all non-empty subsets of group G ′ can establish generalized approximations in group G based on the set-valued mapping T .In this study, we introduce the notion of near-generalized approximations in a group based on set-valued mapping, an extension of the concept of generalized approximations in a group based on set-valued mapping and near approximations in a group.We then present some properties of nearby subgroups in a group based on set-valued mapping.Furthermore, we compare these types of near-generalized and generalized approximations in a group based on set-valued mapping.