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Double-Framed Soft Set Theory Applied to Abel-Grassmann’s Hypergroupoids

Author

Listed:
  • Muhammad Izhar

    (Department of Mathematics, Government College Garhi Kapura Mardan, Khyber Pakhtunkhwa Pakistan)

  • Tariq Mahmood

    (Department of Basic Sciences, University of Engineering and Technology, Taxila, Pakistan)

  • Asghar Khan

    (Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan)

  • Muhammad Farooq

    (Department of Mathematics, Abdul Wali Khan, University Mardan, Khyber Pakhtunkhwa Pakistan)

  • Kostaq Hila

    (Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania)

Abstract

In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids (AG-hypergroupoids). We define double-framed soft AG-hypergroupoids (DFS AG-hypergroupoids) and double-framed soft left (respectively, right) (briefly DFS-left (respectively, DFS-right)) hyperideals of AG-hypergroupoids. It is shown that an idempotent DFS-left hyperideal is a DFS-hyperideal. Also a DFS right hyperideal becomes DFS hyperideal when pure left identity is adjoined to an AG-hypergroupoid, but the converse is not true. We also discuss some properties of these hyperideals in regular AG-hypergroupoids.

Suggested Citation

  • Muhammad Izhar & Tariq Mahmood & Asghar Khan & Muhammad Farooq & Kostaq Hila, 2022. "Double-Framed Soft Set Theory Applied to Abel-Grassmann’s Hypergroupoids," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 819-841, November.
    • Handle: RePEc:wsi:nmncxx:v:18:y:2022:i:03:n:s1793005722500399
    DOI: 10.1142/S1793005722500399
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