Hybrid Ideals in an AG-Groupoid

K. Porselvi (), G. Muhiuddin (), B. Elavarasan, Y. B. Jun () and J. Catherine Grace John ()
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K. Porselvi: Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu 641 114, India
G. Muhiuddin: Department of Mathematics, University of Tabuk, P. O. Box-741, Tabuk 71491, Saudi Arabia
B. Elavarasan: Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu 641 114, India
Y. B. Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
J. Catherine Grace John: Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, Tamil Nadu 641 114, India

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 01, 289-305

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.

Keywords: hybrid structure; AG-groupoid; hybrid product; hybrid idempotent; hybrid ideal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500084

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