{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T20:30:24Z","timestamp":1777321824716,"version":"3.51.4"},"reference-count":79,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000},"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>Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig\u2019s method. To compare the influence of various normalization methods in both the EWM and Hellwig\u2019s method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries\u2019 realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max\u2013min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig\u2019s method. The results are compared with the outcome obtained by Hellwig\u2019s method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig\u2019s method results.<\/jats:p>","DOI":"10.3390\/e26050365","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T08:18:27Z","timestamp":1714119507000},"page":"365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["Impact of Normalization on Entropy-Based Weights in Hellwig\u2019s Method: A Case Study on 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\/0000-0001-9485-6667","authenticated-orcid":false,"given":"Tomasz","family":"Wachowicz","sequence":"additional","affiliation":[{"name":"Department of Operations Research, University of Economics in Katowice, 1 Maja 50, 40-287 Katowice, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"key":"ref_1","unstructured":"Ehrgott, M., and Greco, S. 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