A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras
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 log...
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MDPI AG
2025-04-01
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| author | Ravi Kumar Bandaru Rajesh Neelamegarajan Tahsin Oner Amal S. Alali |
| author_facet | Ravi Kumar Bandaru Rajesh Neelamegarajan Tahsin Oner Amal S. Alali |
| author_sort | Ravi Kumar Bandaru |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6d7fdab35d4841b68276fa5e6a1e61e3 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-6d7fdab35d4841b68276fa5e6a1e61e32025-08-20T03:47:48ZengMDPI AGAxioms2075-16802025-04-0114534710.3390/axioms14050347A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-AlgebrasRavi Kumar Bandaru0Rajesh Neelamegarajan1Tahsin Oner2Amal S. Alali3Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, IndiaDepartment of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamil Nadu, IndiaDepartment of Mathematics, Faculty of Science, Ege University, 35100 Izmir, TürkiyeDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaThis 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.https://www.mdpi.com/2075-1680/14/5/347Sheffer stroke (BCK-algebra)BCK-idealintuitionistic fuzzy SBCK-subalgebraintuitionistic fuzzy SBCK-ideal |
| spellingShingle | Ravi Kumar Bandaru Rajesh Neelamegarajan Tahsin Oner Amal S. Alali A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras Axioms Sheffer stroke (BCK-algebra) BCK-ideal intuitionistic fuzzy SBCK-subalgebra intuitionistic fuzzy SBCK-ideal |
| title | A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras |
| title_full | A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras |
| title_fullStr | A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras |
| title_full_unstemmed | A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras |
| title_short | A New Perspective on Intuitionistic Fuzzy Structures in Sheffer Stroke BCK-Algebras |
| title_sort | new perspective on intuitionistic fuzzy structures in sheffer stroke bck algebras |
| topic | Sheffer stroke (BCK-algebra) BCK-ideal intuitionistic fuzzy SBCK-subalgebra intuitionistic fuzzy SBCK-ideal |
| url | https://www.mdpi.com/2075-1680/14/5/347 |
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