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Lukasiewicz Fuzzy Set Theory Applied to SBE-Algebras

Author

Listed:
  • Tahsin Oner

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

  • Hashem Bordbar

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

  • Neelamegarajan Rajesh

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

  • Akbar Rezaei

    (Department of Mathematics, Payame Noor University, Tehran P.O. Box 19395-4697, Iran)

Abstract

In this paper, we utilize the Lukasiewicz t -norm to construct a novel class of fuzzy sets, termed ζ -Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-algebras). We introduce and examine the concepts of ζ -Lukasiewicz fuzzy SBE-subalgebras and ζ -Lukasiewicz fuzzy SBE-ideals, with a focus on their algebraic properties. Furthermore, we define three specific types of subsets, referred to as ∈-sets, q -sets, and O -sets, and investigate the necessary conditions for these subsets to constitute subalgebras or ideals within the SBE-algebraic context.

Suggested Citation

  • Tahsin Oner & Hashem Bordbar & Neelamegarajan Rajesh & Akbar Rezaei, 2025. "Lukasiewicz Fuzzy Set Theory Applied to SBE-Algebras," Mathematics, MDPI, vol. 13(19), pages 1-25, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3203-:d:1765603
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