Hybrid Ideals in an AG-Groupoid

Abstract

In general, models of universe problems in almost all fields, such as engineering, mathematics, medical sciences, computer science, physics, management sciences, artificial intelligence, and operations research, are practically full of complexities and include various types of uncertainties when dealing with them on numerous occasions. Different theories, such as probability, rough sets, fuzzy sets, soft ideals, and so on, have been created to deal with these uncertainties. An algebraic structure, AG-groupoid, is an intermediate structure between two types of structures: commutative semigroup and groupoid. This structure has a very close relationship to a commutative semigroup since a commutative AG-groupoid is always a semigroup. These structures have so many applications in flocks theory, geometry, topology, and many more. We explore several structural properties of an AG-groupoid by using hybrid structures in this paper. The main motivation behind this paper is to present the concepts of hybrid ideals, hybrid bi-ideals and hybrid interior ideals of an AG-groupoid and characterize AG-groupoid in terms of hybrid structures. Also, we show that the hybrid intersection and hybrid product structures will coincide under certain conditions.