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

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...

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Bibliographic Details
Published in:Scientific reports 2024-01, Vol.14 (1), p.2446-14, Article 2446
Main Authors: Bashir, Shahida, Alharbi, Talal, Mazhar, Rabia, Khalid, Issra, ul Hassan Afzal, Muneeb, Riaz Chaudhry, Nauman
Format: Article
Language:English
Subjects:
639/166
639/705
Algebra
Decision making
Fuzzy sets
Humanities and Social Sciences
multidisciplinary
Science
Science (multidisciplinary)
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-023-49395-5