Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm

Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm

In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><sem...

Full description

Saved in:
Bibliographic Details
Main Authors: Ravikumar Bandaru, Tahsin Oner, Neelamegarajan Rajesh, Amal S. Alali
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
Sheffer stroke (NMV-algebra)
SSNMV-filter
<named-content content-type="inline-formula"><inline-formula> <mml:math id="mm111115"> <mml:semantics> <mml:mi mathvariant="fraktur">T</mml:mi> </mml:semantics> </mml:math> </inline-formula> </named-content>-fuzzy subalgebra
<named-content content-type="inline-formula"> <inline-formula> <mml:math id="mm23335"> <mml:semantics> <mml:mi mathvariant="fraktur">T</mml:mi> </mml:semantics> </mml:math></inline-formula> </named-content>-fuzzy filter
Online Access:https://www.mdpi.com/2227-7390/13/8/1282
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">T</mi></semantics></math></inline-formula>-fuzzy subalgebras and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">T</mi></semantics></math></inline-formula>-fuzzy filters, analyze their properties, and provide several illustrative examples. Our study demonstrates that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">T</mi></semantics></math></inline-formula>-fuzzy subalgebras and filters generalize classical subalgebras and filters, with level subsets preserving algebraic structures under t-norms. Notably, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">T</mi></semantics></math></inline-formula>-fuzzy sets exhibit strong closure properties, and homomorphisms between SSNMV-algebras extend naturally to fuzzy settings. Furthermore, we examine the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">T</mi></semantics></math></inline-formula>-fuzzy subalgebras (or filters) and their classical counterparts, as well as their corresponding level subsets and homomorphisms. These results contribute to refined uncertainty modeling in logical systems, with potential applications in fuzzy control and AI.
ISSN:2227-7390

Similar Items