Lukasiewicz Fuzzy Set Theory Applied to SBE-Algebras

Tahsin Oner, Hashem Bordbar (), Neelamegarajan Rajesh and Akbar Rezaei
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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

Mathematics, 2025, vol. 13, issue 19, 1-25

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.

Keywords: BE-algebra; SBE-algebra; Lukasiewicz fuzzy set; Lukasiewicz fuzzy SBE-subalgebra; Lukasiewicz fuzzy SBE-ideal; ∈-set; q -set; O -set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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