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

Shahida Bashir, Sundas Shahzadi, Ahmad N. Al-Kenani and Muhammad Shabir
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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

Mathematics, 2021, vol. 9, issue 17, 1-18

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.

Keywords: m -PF subsemigroups; m -PF generalized bi-ideals; m -PF bi-ideals; m -PF quasi-ideals; m -PF interior ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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