Artificial Intelligence (AI) has become one of the most transformative technologies of the twenty-first century, significantly influencing governance, healthcare, education, finance, employment, transportation, and public service delivery. As AI-driven systems become increasingly integrated into decision-making processes, concerns have emerged regarding their potential to reinforce existing socio-economic inequalities through algorithmic bias, unequal digital access, and technological exclusion. These challenges are particularly significant for marginalized communities in developing countries such as India, where disparities in digital infrastructure, education, income, and technological literacy continue to limit equitable participation in the AI-driven economy.

While numerous studies have examined Artificial Intelligence from technological, economic, and ethical perspectives, relatively few have developed rigorous mathematical frameworks for measuring AI-induced social exclusion. Existing assessments largely rely on qualitative indicators or descriptive statistical methods, which often fail to capture the complex interactions among socio-economic, technological, institutional, and behavioural variables. Consequently, there is a growing need for robust mathematical models capable of quantifying social exclusion, predicting vulnerable populations, optimizing policy interventions, and evaluating the effectiveness of inclusive AI strategies.

The present study develops mathematical models for measuring AI-induced social exclusion by integrating statistical modelling, fuzzy set theory, graph theory, optimization techniques, probability theory, and machine learning algorithms. A comprehensive Artificial Intelligence Social Exclusion Index (AISEI) is proposed to quantify the degree of exclusion experienced by individuals and communities based on multidimensional indicators including digital accessibility, AI literacy, internet connectivity, educational attainment, economic status, algorithmic fairness, and access to AI-enabled public services.

The research further develops predictive models using regression analysis, decision trees, random forests, support vector machines, gradient boosting algorithms, and artificial neural networks to estimate the probability of AI exclusion among different socio-economic groups. Optimization models are employed to determine equitable allocation of digital infrastructure and AI resources under budgetary constraints, while graph-theoretic models are utilized to analyse patterns of digital connectivity and identify structurally isolated communities. Fuzzy mathematical models are incorporated to address uncertainty and imprecision associated with socio-economic indicators, enabling more realistic assessment of AI accessibility.

The proposed mathematical framework is validated using empirical data collected from marginalized communities across India. Model performance is evaluated using standard statistical and machine learning validation measures including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Receiver Operating Characteristic (ROC) curves, Area Under the Curve (AUC), precision, recall, F1-score, and cross-validation techniques. Sensitivity analysis and Monte Carlo simulations are further conducted to examine the robustness of the proposed models under varying socio-economic conditions.

The findings are expected to contribute significantly to the fields of applied mathematics, mathematical modelling, artificial intelligence, and public policy by providing a scientifically rigorous framework for measuring digital inequality and AI-induced social exclusion. The proposed models will assist policymakers in identifying vulnerable populations, optimizing resource allocation, designing equitable AI policies, and promoting inclusive digital development. Ultimately, the study demonstrates how mathematical modelling can serve as an effective tool for ensuring that technological advancement contributes to social justice, sustainable development, and equitable participation in the emerging AI-driven society.

Keywords: Artificial Intelligence, Mathematical Modelling, Social Exclusion, Fuzzy Mathematics, Optimization, Machine Learning, Graph Theory, Digital Inclusion, AI Fairness, Social Exclusion Index.