ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

Evaluating essential vitamins: a modern approach integrating data and decision-making techniques

Muhammad Waheed Rasheed, Abid Mahboob, Warda Noman, and Kang Yanmei

Department of Mathematics, COMSATS University Islamabad, Vehari, Pakistan

E-mail: waheedrasheed461@gmail.com

Received: 30 March 2025  Accepted: 2 July 2025

Abstract:

This study evaluates 13 essential vitamins using multi-criteria decision-making (MCDM) techniques combined with objective weighting methods. Phase I calculates irregular topological neighbourhood invariants, while Phase II integrates the PIV and ARAS MCDM approaches with five weighting methods (LOPCOW, CRITIC, MEAN, MEREC, and entropy). Results show that the CRITIC method yields the highest variance in criterion weights (\(69.077\times\)), while LOPCOW exhibits the least (\(0.793\times\)). Spearman’s rank correlation analysis confirms strong consistency in rankings (\(\rho = 0.9396{-}1.000\)), with Cobalamin and nicotinic acid emerging as top compounds under PIV and ARAS, respectively. The proposed framework effectively reduces inconsistency in rankings, providing a robust tool for vitamin evaluation based on topological indices and physicochemical properties.

Keywords: Mathematical chemistry; Chemical graph theory; Vitamins; Neighbourhood irregular topological invariants; Multi-criteria decision-making (MCDM)

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04234-x

Chemical Papers 79 (10) 6921–6933 (2025)