{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T14:28:13Z","timestamp":1780583293208,"version":"3.54.1"},"reference-count":74,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T00:00:00Z","timestamp":1707177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development of Brazil (CNPq)","doi-asserted-by":"publisher","award":["311922\/2021-0"],"award-info":[{"award-number":["311922\/2021-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development of Brazil (CNPq)","doi-asserted-by":"publisher","award":["314800\/2021-2"],"award-info":[{"award-number":["314800\/2021-2"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development of Brazil (CNPq)","doi-asserted-by":"publisher","award":["303733\/2019-5"],"award-info":[{"award-number":["303733\/2019-5"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development of Brazil (CNPq)","doi-asserted-by":"publisher","award":["151518\/2022-0"],"award-info":[{"award-number":["151518\/2022-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This research offers a solution to a highly recognized and controversial problem within the composite indicator literature: sub-indicators weighting. The research proposes a novel hybrid weighting method that maximizes the discriminating power of the composite indicator with objectively defined weights. It considers the experts\u2019 uncertainty concerning the conceptual importance of sub-indicators in the multidimensional phenomenon, setting maximum and minimum weights (constraints) in the optimization function. The hybrid weighting scheme, known as the SAW-Max-Entropy method, avoids attributing weights that are incompatible with the multidimensional phenomenon\u2019s theoretical framework. At the same time, it reduces the influence of assessment errors and judgment biases on composite indicator scores. The research results show that the SAW-Max-Entropy weighting scheme achieves greater discriminating power than weighting schemes based on the Entropy Index, Expert Opinion, and Equal Weights. The SAW-Max-Entropy method has high application potential due to the increasing use of composite indicators across diverse areas of knowledge. Additionally, the method represents a robust response to the challenge of constructing composite indicators with superior discriminating power.<\/jats:p>","DOI":"10.3390\/e26020143","type":"journal-article","created":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T03:22:31Z","timestamp":1707189751000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["The Use of Information Entropy and Expert Opinion in Maximizing the Discriminating Power of Composite Indicators"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1411-0553","authenticated-orcid":false,"given":"Matheus Pereira","family":"Lib\u00f3rio","sequence":"first","affiliation":[{"name":"Graduate Program in Computer Science, Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-901, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roxani","family":"Karagiannis","sequence":"additional","affiliation":[{"name":"Center for Planning and Economic Research, 11 Amerikis Str., 10672 Athens, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5649-7736","authenticated-orcid":false,"given":"Alexandre Magno Alvez","family":"Diniz","sequence":"additional","affiliation":[{"name":"Graduate Program in Geography, Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-901, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6372-2316","authenticated-orcid":false,"given":"Petr Iakovlevitch","family":"Ekel","sequence":"additional","affiliation":[{"name":"Graduate Program in Computer Science, Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-901, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Douglas Alexandre Gomes","family":"Vieira","sequence":"additional","affiliation":[{"name":"Graduate Program in Mathematical Modeling, Federal Center of Technological Education of Minas Gerais, Belo Horizonte 30421-169, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura Cozzi","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Graduate Program in Computer Science, Pontifical Catholic University of Minas Gerais, Belo Horizonte 30535-901, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,6]]},"reference":[{"key":"ref_1","unstructured":"Nardo, M., Saisana, M., Saltelli, A., and Tarantola, S. 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