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

**Shahida Bashir 1,\*, Sundas Shahzadi 1, Ahmad N. Al-Kenani 2 and Muhammad Shabir 3**

	- 3 Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan; mshabirbhatti@qau.edu.pk
	- **\*** Correspondence: shahida.bashir@uog.edu.pk

**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

**MSC:** 03E72; 18B40
