Scientific Reports (Jan 2024)

An efficient approach to study multi-polar fuzzy ideals of semirings

  • Shahida Bashir,
  • Talal Alharbi,
  • Rabia Mazhar,
  • Issra Khalid,
  • Muneeb ul Hassan Afzal,
  • Nauman Riaz Chaudhry

DOI
https://doi.org/10.1038/s41598-023-49395-5
Journal volume & issue
Vol. 14, no. 1
pp. 1 – 14

Abstract

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Abstract The multi polar fuzzy (m-PF) set has an extensive range of implementations in real world problems related to the multi-polar information, multi-index and multi-attributes data. This paper introduces innovative extensions to algebraic structures. We present the definitions and some important results of m-polar fuzzy subsemirings (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings. The main contributions of the paper include the derivation and proof of key theorems that shed light on the algebraic interplay and computational aspects of m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings along with examples. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semirings by the properties of these ideals.