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Exploring Fuzzy Filters and Ideals in BG-Algebras: A Comprehensive Framework for Maximal Extensions and Algebraic Generalizations

by Faisal Mehmood, Heng Liu
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 187 - Number 5
Year of Publication: 2025
Authors: Faisal Mehmood, Heng Liu
10.5120/ijca2025924916

Faisal Mehmood, Heng Liu . Exploring Fuzzy Filters and Ideals in BG-Algebras: A Comprehensive Framework for Maximal Extensions and Algebraic Generalizations. International Journal of Computer Applications. 187, 5 ( May 2025), 1-17. DOI=10.5120/ijca2025924916

@article{ 10.5120/ijca2025924916,
author = { Faisal Mehmood, Heng Liu },
title = { Exploring Fuzzy Filters and Ideals in BG-Algebras: A Comprehensive Framework for Maximal Extensions and Algebraic Generalizations },
journal = { International Journal of Computer Applications },
issue_date = { May 2025 },
volume = { 187 },
number = { 5 },
month = { May },
year = { 2025 },
issn = { 0975-8887 },
pages = { 1-17 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume187/number5/exploring-fuzzy-filters-and-ideals-in-bg-algebras-a-comprehensive-framework-for-maximal-extensions-and-algebraic-generalizations/ },
doi = { 10.5120/ijca2025924916 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2025-05-29T00:02:58+05:30
%A Faisal Mehmood
%A Heng Liu
%T Exploring Fuzzy Filters and Ideals in BG-Algebras: A Comprehensive Framework for Maximal Extensions and Algebraic Generalizations
%J International Journal of Computer Applications
%@ 0975-8887
%V 187
%N 5
%P 1-17
%D 2025
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The work incorporates fuzzy set theory in the context of BGalgebras, defining fuzzy filters and ideals which allow the preservation of operations of BG-algebras despite partial membership. This consolidation is vital to ensure that classical algebraic fundamentals remain relevant even in the context of fuzziness. Furthermore, the work provides such a theory for the more advanced maximal fuzzy filters, whose closure properties are essential in the broader design of the theory with Zorn’s Lemma. It also investigates mapping properties and provides numerous examples of fuzzy filters, ideals and complemented fuzzy filters, symmetric and bounded fuzzy filters and ideals. The paper also introduces fuzzy prime filters that are a tool for re-evaluating the algebraic behavior of BG-algebras. The results provided by this paper gives a complete framework to understand all BG-algebras as well as a generalization of them in fuzzy algebraic systems. This theoretical framework not only contributes to the field of algebra, but may also serve as a precursor for applications in domains like fuzzy logic, decision-making, and computing systems. The further investigation of closure properties, maximal extensions and structural relationships may pave an interesting path for both theory and practice.

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Index Terms

Computer Science
Information Sciences

Keywords

BG-algebra fuzzy filters fuzzy ideals maximal fuzzy filters fuzzy prime filters

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