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Keywords = Sheffer stroke (BCK-algebra)

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16 pages, 274 KiB  
Article
A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras
by Ravi Kumar Bandaru, Rajesh Neelamegarajan, Tahsin Oner and Amal S. Alali
Axioms 2025, 14(5), 347; https://doi.org/10.3390/axioms14050347 - 30 Apr 2025
Viewed by 287
Abstract
This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer [...] Read more.
This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for understanding the interaction between intuitionistic logic and Sheffer stroke BCK-algebras. The paper establishes a connection between subalgebras and level sets in the framework of Sheffer stroke BCK-algebras, demonstrating that the level set of intuitionistic fuzzy SBCK-subalgebras corresponds precisely to their subalgebras, and conversely. Additionally, the study provides novel results regarding the structural properties of Sheffer stroke BCK-algebras under intuitionistic fuzzy logic, specifically focusing on the conditions under which fuzzy sets become SBCK-subalgebras or SBCK-ideals. This work contributes to the theoretical foundations of fuzzy logic in algebraic structures, offering a deeper understanding of the interplay between intuitionistic fuzzy sets and the algebraic operations within Sheffer stroke BCK-algebras. Full article
(This article belongs to the Section Algebra and Number Theory)
27 pages, 333 KiB  
Article
Bipolar Fuzzy Sheffer Stroke in BCK-Algebras
by Tahsin Oner, Rajesh Neelamegarajan, Ravi Kumar Bandaru and Amal S. Alali
Axioms 2025, 14(5), 331; https://doi.org/10.3390/axioms14050331 - 26 Apr 2025
Viewed by 345
Abstract
In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures within this algebraic context. We demonstrate a bidirectional [...] Read more.
In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures within this algebraic context. We demonstrate a bidirectional relationship between SBCK-subalgebras and their level sets, proving that each level set derived from a bipolar fuzzy SBCK-subalgebra constitutes a subalgebra, and, conversely, each such subalgebra defines an associated level set. This duality emphasizes the structural interplay between bipolar fuzzy logic and the Sheffer stroke operation in BCK-algebras. Full article
(This article belongs to the Section Algebra and Number Theory)
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