<p>The increasing prevalence of social media addiction among adolescents has become a significant concern, often exceeding other harmful behaviors. Evaluating the addictive potential of various platforms is challenging due to the diversity of applications and the subjectivity inherent in expert judgments. To address these complexities, this study proposes a novel distance measure within the Pythagorean fuzzy set framework, designed to overcome the limitations of existing measures, which often yield inaccurate or inconsistent results in specific contexts. To support the mathematical validity of the proposed measure, its geometric behavior is analyzed, and a comparative study with existing distance functions is conducted using numerical examples. A comprehensive multi-criteria decision-making framework is then developed, incorporating the method based on the removal effects of criteria (MEREC) for objective weighting and stepwise weight assessment ratio analysis (SWARA) for subjective weighting. These weights are integrated using the technique for order of preference by similarity to the ideal solution (TOPSIS) to rank social media platforms based on their addiction potential. Sensitivity and comparative analyses confirm the robustness, reliability, and consistency of the proposed approach. The study concludes by demonstrating the advantages of the framework and identifying potential directions for future research.</p>