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.