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

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

doi:10.3390/math9172031

Shahida Bashir, Ahmad N Al-Kenani + Show 2 more

Open Access

https://doi.org/10.3390/math9172031

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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.

Highlights

We have proved that every m-polar fuzzy bi-ideals (m-PFBIs) of
The structure of semigroups is investigated using the idea of m-polar fuzzy set (m-PFS) in this research paper
We proved some results related to fuzzy ideals in semigroups in terms of m-polar fuzzy ideals (m-PFIs) in semigroups

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The m-PFS has an extensive range of implementations in real world problems related to the multiagent, multi-objects, multi-polar information, multi-index and multi-attributes. This theory is applicable when a company decides to construct an item, a country elects its political leaders, or a group of friends wants to visit a country, with various options. Zadeh [10] was the first to propose fuzzy set theory as a solution to such complicated issues. By extending the work of [24,27], the concept of m-PFIs in semigroups was introduced and characterizations of regular and intra-regular semigroups according to the properties of m-PFIs are given in this paper.

Preliminaries

Characterization of Semigroups by m-Polar Fuzzy Sets

Comparative Study and Discussion

Conclusions