{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T16:21:34Z","timestamp":1774974094434,"version":"3.50.1"},"reference-count":80,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,25]],"date-time":"2024-02-25T00:00:00Z","timestamp":1708819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bialystok University of Technology","award":["WZ\/WI-IIT\/2\/22"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/22"]}]},{"name":"Ministry of Education and Science","award":["WZ\/WI-IIT\/2\/22"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e26030197","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T06:50:23Z","timestamp":1708930223000},"page":"197","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Extended Hellwig\u2019s Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating Sustainable Development in the Education Area"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2249-7217","authenticated-orcid":false,"given":"Ewa","family":"Roszkowska","sequence":"first","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-4063","authenticated-orcid":false,"given":"Marzena","family":"Filipowicz-Chomko","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6011-7855","authenticated-orcid":false,"given":"Anna","family":"\u0141yczkowska-Han\u0107kowiak","sequence":"additional","affiliation":[{"name":"Institute of Economics and Finance, WSB Merito University in Pozna\u0144, Ul. Powsta\u0144c\u00f3w Wielkopolskich 5, 61-895 Pozna\u0144, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2914-7941","authenticated-orcid":false,"given":"El\u017cbieta","family":"Majewska","sequence":"additional","affiliation":[{"name":"Faculty of Economics and Finance, University of Bialystok, Warszawska 63, 15-062 Bialystok, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Figueira, E.M., and Greco, S. (2005). Multiple Criteria Decision Analysis: State of the Art Surveys, Springer Science + Business Media.","DOI":"10.1007\/b100605"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Roy, B. (1996). Multicriteria Methodology for Decision Aiding, Kluwer Academic Publisher.","DOI":"10.1007\/978-1-4757-2500-1"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Triantaphyllou, E. (2000). Multi-Criteria Decision Making Methods: A Comparative Study, Springer. 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