An integrative MCDM framework using topological indices for ranking vitamins based on solubility properties

This study presents a novel, integrated framework that combines graph-theoretic topological indices with multi-criteria decision-making (MCDM) techniques to systematically rank vitamins based on their solubility properties. The molecular structures of eleven essential vitamins were translated into quantitative descriptors using six distinct topological indices, which serve as proxies for key physicochemical properties governing solubility. These indices were then employed as criteria within three well-established MCDM methods: VIKOR, TOPSIS, and SAW to generate robust rankings. To ensure comprehensive and unbiased analysis, four contrasting weighting strategies (point allocation, standard deviation, entropy, and mean weight) were utilized to determine the relative importance of each criterion. The results demonstrate a high degree of consensus across methodologies, consistently identifying $\alpha$ -tocopherol (vitamin E) and nicotinic acid (niacin) as the top- and bottom-ranked vitamins, respectively, while revealing nuanced differences in the mid-tier rankings based on the chosen MCDM approach and weighting scheme. This work underscores the significant potential of integrating computational chemistry with decision science to solve complex ranking problems in nutrition and pharmacology. The proposed framework offers a powerful, transparent, and reproducible tool for optimizing vitamin selection in dietary formulation and pharmaceutical design, paving the way for its application to other classes of compounds.