Regular and Intra-Regular Semigroups in Terms of <i>m</i>-Polar Fuzzy Environment

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

Format: Article
Diterbitkan: MDPI AG 2021-08-01

Deskripsi

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