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, Mohammed Elgarhy- General Mathematics
- Engineering (miscellaneous)
- Computer Science (miscellaneous)
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.