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

Author

Listed:
  • Ravikumar Bandaru

    (Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, India)

  • Tahsin Oner

    (Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey)

  • Neelamegarajan Rajesh

    (Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamilnadu, India)

  • Amal S. Alali

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

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 T -fuzzy subalgebras and T -fuzzy filters, analyze their properties, and provide several illustrative examples. Our study demonstrates that T -fuzzy subalgebras and filters generalize classical subalgebras and filters, with level subsets preserving algebraic structures under t-norms. Notably, T -fuzzy sets exhibit strong closure properties, and homomorphisms between SSNMV-algebras extend naturally to fuzzy settings. Furthermore, we examine the relationships between T -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.

Suggested Citation

  • Ravikumar Bandaru & Tahsin Oner & Neelamegarajan Rajesh & Amal S. Alali, 2025. "Fuzzy Sets in Strong Sheffer Stroke NMV-Algebra with Respect to a Triangular Norm," Mathematics, MDPI, vol. 13(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1282-:d:1634253
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