Sheffer Stroke BCK-Algebras via Linear Diophantine Fuzzy Structures
Articles > Article · 2026
Authors: Amal S. Alali, Tahsin ÖNER, Ravikumar Bandaru, Neelamegarajan Rajesh, Hashem Bordbar
Axioms, Journal Indexed in SCI Expanded, International, WoS, 2026, vol 15, pp 86-86
Summary
This study investigates linear Diophantine fuzzy structures within the framework of Sheffer stroke BCK-algebras (SBCK-algebras). We introduce and characterize linear Diophantine fuzzy SBCK-subalgebras and linear Diophantine fuzzy SBCK-ideals, establishing fundamental connections between these fuzzy structures and their corresponding crisp subalgebras and ideals. In particular, we prove that the level sets of linear Diophantine fuzzy SBCK-subalgebras form SBCK-subalgebras, and, conversely, every SBCK-subalgebra gives rise to such a fuzzy structure. Additionally, we show that every linear Diophantine fuzzy SBCK-ideal induces a linear Diophantine fuzzy SBCK-subalgebra; however, the converse does not necessarily hold. Several structural properties, homomorphic images, and intersections of such fuzzy ideals are also examined. These results demonstrate how linear Diophantine logic naturally integrates with Sheffer stroke BCK-algebras and enriches their algebraic behavior.