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

Author

Listed:
  • Asmat Hadi

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
    Department of Statistics, Abdul Wali Khan University, Mardan 23200, Pakistan
    These authors contributed equally to this work.)

  • Asghar Khan

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Asmat Hadi & Asghar Khan & Nosheen Faiz & Dost Muhammad Khan & Rashad A. R. Bantan & Mohammed Elgarhy, 2023. "Exploring Hybrid H-bi-Ideals in Hemirings: Characterizations and Applications in Decision Making," Mathematics, MDPI, vol. 11(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3683-:d:1225959
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    References listed on IDEAS

    as
    1. G. Muhiuddin & D. Al-Kadi & A. Mahboob & Ali Jaballah, 2020. "Hybrid Structures Applied to Ideals in BCI-Algebras," Journal of Mathematics, Hindawi, vol. 2020, pages 1-7, November.
    2. Abid Khan & Miin-Shen Yang & Mirajul Haq & Ashfaq Ahmad Shah & Muhammad Arif, 2022. "A New Approach for Normal Parameter Reduction Using σ -Algebraic Soft Sets and Its Application in Multi-Attribute Decision Making," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
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