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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Secure and transparent artificial intelligence through uncertainty-infused algebraic frameworks

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pp. 1125–1134Vol. 29Issue 2-BFebruary 2026DOI: 10.47974/JDMSC-2652 Crossmark XML
Received:
14 May 2025
Published Online:
16 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2652
Pages:
1125–1134

Abstract

Explainable Artificial Intelligence (XAI) increasingly demands mathematically grounded frameworks that not only enhance transparency and interpretability but also ensure computational security and trust. Existing explainability methods often rely on post-hoc approximations that lack both structural rigor and security assurance. This work introduces an uncertainty-infused algebraic framework that extends classical algebraic systemssuch as groups, rings, and latticesby embedding probabilistic and fuzzy semantics directly into their operational structure. The proposed formulation enables the structured representation and manipulation of ambiguous or incomplete information while maintaining interpretability through mathematically traceable transformations.By integrating uncertainty within algebraic foundations, the framework bridges symbolic reasoning and data-driven learning, offering a unified approach that enhances both transparency and resilience against adversarial or inconsistent transformations. Moreover, the algebraic traceability of uncertain computations contributes to security-aware interpretability, enabling the detection of anomalous operations and ensuring reliable model reasoning. Demonstrations across interpretable neural architectures, symbolic reasoning, and knowledge graphs highlight the potential of this approach to strengthen robustness, semantic clarity, and computational integrity. This theoretical contribution provides a rigorous mathematical pathway toward the design of transparent, interpretable, and secure AI systems grounded in uncertainty-aware algebraic principles.

Keywords

Uncertainty-aware algebraic structureExplainable artificial intelligence (XAI)Interpretable and secure machine learningAlgebraic reasoning

Subject Classifications

68Q85

References

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