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Regular and Intra-Regular Semigroups in Terms of m -Polar Fuzzy Environment

Author

Listed:
  • Shahida Bashir

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan)

  • Sundas Shahzadi

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan)

  • Ahmad N. Al-Kenani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia)

  • Muhammad Shabir

    (Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan)

Abstract

The central objective of the proposed work in this research is to introduce the innovative concept of an m -polar fuzzy set ( m -PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m -PFSs. This paper provides some important results related to m -polar fuzzy subsemigroups ( m -PFSSs), m -polar fuzzy ideals ( m -PFIs), m -polar fuzzy generalized bi-ideals ( m -PFGBIs), m -polar fuzzy bi-ideals ( m -PFBIs), m -polar fuzzy quasi-ideals ( m -PFQIs) and m -polar fuzzy interior ideals ( m -PFIIs) in semigroups. This research paper shows that every m -PFBI of semigroups is the m -PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m -PFIs and characterizes regular and intra-regular semigroups by the properties of m -PFIs and m -PFBIs.

Suggested Citation

  • Shahida Bashir & Sundas Shahzadi & Ahmad N. Al-Kenani & Muhammad Shabir, 2021. "Regular and Intra-Regular Semigroups in Terms of m -Polar Fuzzy Environment," Mathematics, MDPI, vol. 9(17), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2031-:d:620790
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    References listed on IDEAS

    as
    1. Shahida Bashir & Medhit Fatima & Muhammad Shabir, 2019. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    2. Muhammad Athar Mehmood & Muhammad Akram & Majed G. Alharbi & Shahida Bashir, 2021. "Solution of Fully Bipolar Fuzzy Linear Programming Models," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-31, April.
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