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...
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2025-04-01
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| author | Ravikumar Bandaru Tahsin Oner Neelamegarajan Rajesh Amal S. Alali |
| author_facet | Ravikumar Bandaru Tahsin Oner Neelamegarajan Rajesh Amal S. Alali |
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| description | 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. |
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| publishDate | 2025-04-01 |
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| spelling | doaj-art-8388716b84564d5db02e7e8b87ce021e2025-08-20T02:28:32ZengMDPI AGMathematics2227-73902025-04-01138128210.3390/math13081282Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular NormRavikumar Bandaru0Tahsin Oner1Neelamegarajan Rajesh2Amal S. Alali3Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, IndiaDepartment of Mathematics, Faculty of Science, Ege University, 35100 Izmir, TurkeyDepartment of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, IndiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaIn 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.https://www.mdpi.com/2227-7390/13/8/1282Sheffer 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 |
| spellingShingle | Ravikumar Bandaru Tahsin Oner Neelamegarajan Rajesh Amal S. Alali Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm Mathematics 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 |
| title | Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm |
| title_full | Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm |
| title_fullStr | Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm |
| title_full_unstemmed | Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm |
| title_short | Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm |
| title_sort | fuzzy sets in strong sheffer stroke nmv algebra with respect to a triangular norm |
| topic | 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 |
| url | https://www.mdpi.com/2227-7390/13/8/1282 |
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