Exploring Hybrid H-bi-Ideals in Hemirings: Characterizations and Applications in Decision Making

Asmat Hadi (), Asghar Khan, Nosheen Faiz, Dost Muhammad Khan (), Rashad A. R. Bantan and Mohammed Elgarhy
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Asmat Hadi: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Asghar Khan: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Nosheen Faiz: Department of Statistics, Abdul Wali Khan University, Mardan 23200, Pakistan
Dost Muhammad Khan: Department of Statistics, Abdul Wali Khan University, Mardan 23200, Pakistan
Rashad A. R. Bantan: Department of Marine Geology, Faulty of Marine Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
Mohammed Elgarhy: Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt

Mathematics, 2023, vol. 11, issue 17, 1-24

Abstract: The concept of the hybrid structure, as an extension of both soft sets and fuzzy sets, has gained significant attention in various mathematical and decision-making domains. In this paper, we delve into the realm of hemirings and investigate the properties of hybrid h-bi-ideals, including prime, strongly prime, semiprime, irreducible, and strongly irreducible ones. By employing these hybrid h-bi-ideals, we provide insightful characterizations of h-hemiregular and h-intra-hemiregular hemirings, offering a deeper understanding of their algebraic structures. Beyond theoretical implications, we demonstrate the practical value of hybrid structures and decision-making theory in handling real-world problems under imprecise environments. Using the proposed decision-making algorithm based on hybrid structures, we have successfully addressed a significant real-world problem, showcasing the efficacy of this approach in providing robust solutions.

Keywords: prime; strongly prime; semiprime; irreducible and strongly irreducible hybrid h-bi-ideals; decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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