<p>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 (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11696_2025_4234_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$69.077\times$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>69.077</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation>), while LOPCOW exhibits the least (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11696_2025_4234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$0.793\times$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.793</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation>). Spearman’s rank correlation analysis confirms strong consistency in rankings (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11696_2025_4234_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="127" /> </InlineMediaObject> <EquationSource Format="TEX">$\rho = 0.9396{-}1.000$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.9396</mn> <mo>-</mo> <mn>1.000</mn> </mrow> </math></EquationSource> </InlineEquation>), 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.</p>

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

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发表日期：

2025年7月17日

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

摘要

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 ( $69.077\times$ $69.077 \times$ ), while LOPCOW exhibits the least ( $0.793\times$ $0.793 \times$ ). Spearman’s rank correlation analysis confirms strong consistency in rankings ( $\rho = 0.9396{-}1.000$ $ρ = 0.9396 - 1.000$ ), 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.