Roszkowska Ewa, Filipowicz-Chomko Marzena, Łyczkowska-Hanćkowiak Anna, Majewska Elżbieta
Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland.
Institute of Economics and Finance, WSB Merito University in Poznań, Ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland.
Entropy (Basel). 2024 Feb 25;26(3):197. doi: 10.3390/e26030197.
One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig's method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig's method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria.
多准则决策分析中的关键步骤之一是确定准则的重要性并确定它们之间的关系。本文提出了一种扩展的赫尔维格方法（H_EM），该方法利用基于熵的权重和马氏距离来解决这一问题。通过纳入熵的概念，根据矩阵数据所表示的信息内容来确定权重。马氏距离用于处理准则之间的相互依赖关系，有助于提高所提出框架的性能。为了说明扩展的H_EM方法的相关性和有效性，本研究利用它来评估2021年欧盟国家在实现《2030年议程》可持续发展目标4方面在教育领域的进展。对扩展的赫尔维格方法及其其他变体所获得的结果进行了性能比较。结果表明，根据距离度量（欧几里得或马氏）和权重系统（相等或基于熵）的选择，对欧盟国家在教育领域的排名有重大影响。总体而言，本研究突出了所提出方法在处理具有相互依赖准则的复杂决策场景方面的潜力。
