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Keywords = (Sheffer stroke) Hilbert algebra

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21 pages, 307 KB  
Article
Unifying Bipolar and Cubic Set Theories: Ideals in Sheffer Stroke Hilbert Algebras
by Amal S. Alali, Hashem Bordbar, Ravikumar Bandaru, Rajesh Neelamegarajan and Tahsin Oner
Axioms 2026, 15(5), 301; https://doi.org/10.3390/axioms15050301 - 22 Apr 2026
Viewed by 281
Abstract
In recent years, the study of generalized fuzzy structures in algebraic systems has attracted considerable attention due to their ability to represent uncertainty and bipolar information. In this paper, we introduce the notion of cubic bipolar ideals in the framework of Sheffer stroke [...] Read more.
In recent years, the study of generalized fuzzy structures in algebraic systems has attracted considerable attention due to their ability to represent uncertainty and bipolar information. In this paper, we introduce the notion of cubic bipolar ideals in the framework of Sheffer stroke Hilbert algebras. This concept integrates the descriptive capability of cubic sets with the dual representation of bipolar information, providing a broader perspective for investigating algebraic structures associated with the Sheffer stroke operation. We establish the definition of cubic bipolar ideals and investigate several of their fundamental properties. In particular, the structural behavior of these ideals is examined within Sheffer stroke Hilbert algebras. Furthermore, the preservation of cubic bipolar ideals under algebraic homomorphisms is analyzed through the study of images and preimages. The Cartesian product of cubic bipolar ideals is also discussed, and conditions ensuring the stability of the resulting structures are obtained. The results presented here contribute to the development of fuzzy algebraic theory and extend existing approaches to Sheffer stroke-based algebraic systems. Full article
13 pages, 308 KB  
Article
Sheffer Stroke Hilbert Algebras Stabilizing by Ideals
by Tugce Katican and Hashem Bordbar
Axioms 2024, 13(2), 97; https://doi.org/10.3390/axioms13020097 - 30 Jan 2024
Cited by 4 | Viewed by 2060
Abstract
This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these [...] Read more.
This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterwards, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers. Full article
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