A Novel Mathematical Framework for Trustworthy Artificial Intelligence Using Fuzzy Logic, Topology, and Uncertainty Modelling
Abstract
Artificial Intelligence (AI) has achieved remarkable progress in recent years, enabling advanced decision-making in healthcare, autonomous systems, cybersecurity, natural language processing, and scientific computing. However, the increasing complexity of modern AI models, particularly deep learning architectures, has introduced significant challenges related to interpretability, transparency, robustness, and uncertainty management. Many advanced AI systems operate as black-box models, where the underlying reasoning process behind predictions remains difficult to understand. This limitation restricts their adoption in applications where reliability and accountability are essential. This study proposes a novel mathematical framework for developing trustworthy artificial intelligence by integrating three complementary mathematical approaches: fuzzy logic, topology, and uncertainty modelling. Fuzzy logic provides an interpretable mechanism for representing ambiguous and incomplete information through membership functions and reasoning rules. Topological Data Analysis (TDA) enables the identification of hidden structural relationships and persistent patterns within complex high-dimensional datasets. Uncertainty modelling enhances reliability by estimating prediction confidence and distinguishing between reliable and uncertain outcomes. The proposed fuzzy–topological uncertainty framework aims to move beyond conventional accuracy-oriented AI models by embedding trust-related characteristics directly into the mathematical architecture. The framework combines interpretable reasoning, structural data analysis, and uncertainty-aware prediction within a unified model. A mathematical formulation is developed, and the framework is evaluated conceptually based on interpretability, robustness, and reliability considerations. The proposed approach provides a foundation for designing AI systems that are not only computationally effective but also transparent, explainable, and trustworthy. The framework has potential applications in safety-critical domains including healthcare, autonomous technologies, cybersecurity, and scientific decision-support systems.
How to Cite
Parul , Vishal Saxena, "A Novel Mathematical Framework for Trustworthy Artificial Intelligence Using Fuzzy Logic, Topology, and Uncertainty Modelling", Vol. 4, Issue 5, 28-08-2026, pp. 1-13.
