Near approximations in groups

In this paper, we firstly introduce the notion of a near approximations in a group, which is an extended notion of a rough approximations in a group. Then we define lower and upper near subgroups based on normal subgroups in a group and give some properties of such subgroups. Furthermore, we obtain a comparison between these types of approximations and the approximation introduced by Kuroki and Wang (Inf Sci 90:203–220, 1996). © 2018, Springer-Verlag GmbH Germany, part of Springer Nature