Approximation of soft ideals by soft relations in semigroups

A soft set handles indeterminate data. By using an equivalence relation, Pawlak introduced the rough set concept for dealing uncertainty to approximate a set. Many authors generalized the concept and used binary relations to approximate a set. A soft set is approximated in this paper by soft binary relations in the context of the aftersets and foresets. Along these lines, we get two sets of soft sets, called the lower approximation and upper approximation with respect to the aftersets and foresets. We applied these concepts on semigroups and approximations of soft subsemigroups, soft left (right) ideals, soft interior ideals and soft bi-ideals of semigroups are studied. Moreover, for the illustration of the concept, some examples are considered.