(α,β)-Soft Intersectional Rings and Ideals with their Applications

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called Formula: see text-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define Formula: see text-soft-intersectional ideal and Formula: see text-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on Formula: see text-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and Formula: see text-soft-intersectional ring, soft-intersectional ideal and Formula: see text-soft-intersectional ideal.