On Near-Rings with Soft Union Ideals and Applications

Abstract

In this paper, we define soft union near-ring on a soft set by using soft sets, inclusion relation and union of sets. This new notion functions as a bridge among soft set theory, set theory and near-ring theory. We then derive its basic properties and investigate the relationship between soft intersection near-ring and soft union near-ring. Furthermore, we obtain some analog of classical near-ring theoretic concepts for soft union near-ring and give the applications of soft union near-ring to near-ring theory.