Coarse Set Theory Framework for Ethical AI Decision-Making: Mathematical Foundations and Practical Implementation
Ranadhir Ghosh · 2025
We present a mathematically rigorous framework for ethical AI decision-making that addresses the critical gap between theoretical ethical principles and practical implementation. Our approach introduces Coarse Set Theory (CST) as a unifying mathematical foundation that simultaneously handles multiple ethical constraints while providing formal completeness guarantees. The framework establishes an ethical constraint space equipped with a topology that captures ethical proximity relationships, enabling continuous optimization of ethical decisions. We prove that maximal ethical decision subsets always exist and provide polynomial-time algorithms for their construction. Our experimental validation on the ETHOS benchmark (15,000 ethical scenarios across healthcare, finance, and criminal justice) demonstrates 97.3% ± 0.4% ethical consistency with significant bias reduction (Cohen's d = 1.23, p ¡ 0.001) compared to existing approaches. The framework shows robust performance across cultural contexts and provides interpretable justifications for decisions, making it suitable for deployment in high-stakes applications. We establish theoretical guarantees for robustness against adversarial perturbations and provide a comprehensive governance framework for realworld deployment. This work bridges the gap between ethical theory and practice, offering the first mathematically complete and computationally tractable solution to multi-constraint ethical decision-making in AI systems.