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Extended Hellwig's Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating

Ewa Roszkowska1, Marzena Filipowicz-Chomko1, Anna Łyczkowska-Hanćkowiak2

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Summary

This study introduces an enhanced Hellwig's method (H_EM) using entropy weights and Mahalanobis distance for multi-criteria decision analysis. The method significantly impacts country rankings for education progress, highlighting the importance of chosen metrics.

Keywords:
Euclidean distanceHellwig’s methodMahalanobis distanceeducationentropy-based weightsmulti-criteria decision makingsustainable development

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Area of Science:

  • Decision Sciences
  • Educational Policy Analysis
  • Statistical Modeling

Background:

  • Multi-criteria decision analysis (MCDA) requires robust methods for criterion weighting and dependency handling.
  • Existing methods may not fully capture interdependencies between criteria or utilize information content effectively.
  • Assessing progress towards Sustainable Development Goals (SDGs) necessitates advanced analytical frameworks.

Purpose of the Study:

  • To propose an extended Hellwig's method (H_EM) incorporating entropy-based weights and Mahalanobis distance.
  • To enhance the analysis of criterion importance and interdependencies in MCDA.
  • To evaluate the effectiveness of the H_EM in assessing progress towards Sustainable Development Goal 4 (SDG 4) in the European Union.

Main Methods:

  • Developed an extended Hellwig's method (H_EM) integrating entropy for weight determination based on information content.
  • Employed Mahalanobis distance to account for interdependencies among decision criteria.
  • Applied the H_EM to analyze SDG 4 progress in European Union countries using 2021 education data.

Main Results:

  • The choice of distance measure (Euclidean vs. Mahalanobis) and weighting system (equal vs. entropy-based) significantly altered the ranking of EU countries regarding SDG 4.
  • Entropy-based weights and Mahalanobis distance provided a more nuanced assessment by considering data information content and criterion interdependencies.
  • The extended H_EM demonstrated improved performance in handling complex decision-making scenarios.

Conclusions:

  • The proposed extended Hellwig's method (H_EM) offers a valuable tool for complex MCDA, particularly when criteria are interdependent.
  • Accurate assessment of progress, such as for SDG 4, depends critically on the methodological choices in weighting and distance calculation.
  • The H_EM framework provides a more sophisticated approach to decision-making in fields like educational policy and sustainable development.