Department of Mathematics Urmia University Urmia-Iran
10.22034/jdgaa.2026.2106909.1021
Abstract
This paper introduces a new construction of fuzzy topology on BCK-algebras based on the notion of fuzzy ideals. By defining a fuzzy neighborhood system derived from all fuzzy ideals that assign full membership to a given point, we construct a fuzzy topological structure on a BCK-algebra (X, ∗, 0). A fuzzy set is declared open if it satisfies a continuity-like condition with respect to this neighborhood system. We establish fundamental properties of this topology, including the behavior of fuzzy open sets, the relationship between fuzzy ideals and neighborhoods, and several structural theorems. This work generalizes earlier approaches to topologizing algebraic structures using ideals in the fuzzy setting and provides a framework for further exploration in fuzzy logical algebras.
Shahbazpour, K. (2026). Fuzzy ideal-based topology on bck-algebras. (e743850). Journal of Differential Geometry, Applications and Aspects, (), e743850 https://doi.org/10.22034/jdgaa.2026.2106909.1021
MLA
Shahbazpour, K. "Fuzzy ideal-based topology on bck-algebras" .e743850 , Journal of Differential Geometry, Applications and Aspects, , 2026, e743850. doi: 10.22034/jdgaa.2026.2106909.1021
HARVARD
Shahbazpour, K. (2026). 'Fuzzy ideal-based topology on bck-algebras', Journal of Differential Geometry, Applications and Aspects, (), e743850. doi: 10.22034/jdgaa.2026.2106909.1021
CHICAGO
Shahbazpour, K., "Fuzzy ideal-based topology on bck-algebras." Journal of Differential Geometry, Applications and Aspects, (2026): e743850, doi: 10.22034/jdgaa.2026.2106909.1021
VANCOUVER
Shahbazpour K. Fuzzy ideal-based topology on bck-algebras. JDGAA. 2026;():e743850 (In Persian). doi: 10.22034/jdgaa.2026.2106909.1021
Journal of Differential Geometry, Applications and Aspects