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.
An Explainable Hybrid Deep Learning Framework for Automated Transportation Infrastructure Defect Detection and Predictive Maintenance
Abstract
Transportation infrastructure monitoring is essential for ensuring public safety, improving maintenance efficiency, and extending the operational lifespan of critical assets. Conventional inspection approaches are often labour-intensive, time-consuming, and limited by human subjectivity and environmental constraints. Recent advancements in deep learning and computer vision have enabled automated defect detection; however, existing models frequently suffer from limited generalization, insufficient interpretability, and weak integration with predictive maintenance strategies. This study proposes an explainable hybrid deep learning framework for automated transportation infrastructure defect detection and predictive maintenance. The proposed framework integrates convolutional neural networks (CNNs) for spatial feature extraction with attention-based Transformer mechanisms for capturing complex global feature relationships. An explainable artificial intelligence (XAI) module is incorporated to improve model transparency by identifying the image regions responsible for prediction outcomes. The framework is designed to classify multiple infrastructure defects, including cracks, potholes, corrosion, and surface deterioration, while supporting proactive maintenance decision-making through predictive analysis. Experimental evaluation demonstrates that the proposed approach improves detection accuracy, robustness under varying environmental conditions, and interpretability compared with conventional deep learning approaches. The integration of hybrid learning, explainable AI, and predictive maintenance provides a reliable solution for intelligent infrastructure management. The proposed framework contributes toward the development of safer, sustainable, and data-driven transportation systems by transforming automated inspection from a defect identification process into a comprehensive decision-support mechanism.
