SBE-Algebras via Intuitionistic Fuzzy Structures

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, Thanjavur 613005, Tamil Nadu, India
Akbar Rezaei: Department of Mathematics, Payame Noor University, Tehran P.O. Box 19395-4697, Iran

Mathematics, 2024, vol. 12, issue 24, 1-26

Abstract: The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understanding the behavior of intuitionistic fuzzy logic in this algebraic structure. The study further establishes a bidirectional relationship between subalgebras, ideals, filters, and their respective level sets on Sheffer stroke BE-algebras, demonstrating that the level set of an intuitionistic fuzzy SBE-subalgebra, ideal, or filter is itself a subalgebra, ideal, or filter on this algebra, and vice versa.

Keywords: BE-algebra; Sheffer stroke BE-algebra; BE-ideal; intuitionistic fuzzy SBE-subalgebra; intuitionistic fuzzy SBE-ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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