α-inclusions applied to group theory via soft set and logic

Abstract

Soft set theory, initiated by Molodtsov, is a tool for modeling various types of uncertainty. In this paper, upper and lower α-inclusions of a soft set are defined. By using these new notions, some analyzes with respect to group theory are made and it is shown that some of the subgroups of a group can be obtained easily with the help of these notions. It is also illustrated that a soft int-group and a soft uni-group can be obtained by its upper α-subgroups and lower α-subgroups, respectively. Furthermore, soft int-group by its family of upper α-subgroups is characterized under a certain equivalence relation. Finally, a new method used to construct a soft int-group with the help of its upper α-subgroups are introduced and an application of this method is given.