<p>The rapid development and widespread adoption of data-driven decision-making methods have raised significant concerns regarding their differential impact on various individuals and subgroups, potentially leading to unintended discriminatory outcomes. Such disparities may result in algorithmic bias, undermining social welfare. In response to these challenges, the theory of fair machine learning has emerged as a vital field of research. This paper explores the concept of strong group fairness within machine learning and introduces two novel fairness metrics: strong equal opportunity and strong equalized odds, providing precise definitions and discussing their practical implications. To integrate fairness into the optimization framework, we leverage the optimal transport theory, formulating strong group fairness as a regularization term in the optimization problem, which results in a bilinear optimization problem. Specifically, for the hinge-loss support vector machine (SVM) model, we show that these bilinear optimization problems can be reformulated as mixed-integer linear programming (MILP) problems. Extensive numerical experiments are performed to evaluate the effectiveness of the proposed fairness regularization and validate the MILP reformulation. The results demonstrate that the fairness model with strong equal opportunity regularization strikes an effective balance between accuracy and fairness, and that the MILP reformulation provides superior solution quality compared to traditional alternating minimization methods.</p>