Soft set theory, initiated by Molodtsov, is a tool for modeling various types of uncertainty. In this paper, upper and lower-inclusions of a soft set are de…ned. 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-subgroups and lower-subgroups, respectively. Furthermore, soft int-group by its family of upper-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-subgroups are introduced and an application of this method is given.
In this paper, firstly, information about soft set introduced by Molodtsov is given. Then, the operations on the soft set are introduced. After then a definition of soft uni-k-ideal of a semiring by using the union operation of sets is given. Finally, some algebraic applications by using soft uni-k-ideal are investigated.
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