{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T05:53:48Z","timestamp":1762062828828,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"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\/2022"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/2022"]}]},{"name":"Wroclaw University of Economics and Business","award":["WZ\/WI-IIT\/2\/2022"],"award-info":[{"award-number":["WZ\/WI-IIT\/2\/2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig\u2019s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.<\/jats:p>","DOI":"10.3390\/e24081081","type":"journal-article","created":{"date-parts":[[2022,8,7]],"date-time":"2022-08-07T21:03:50Z","timestamp":1659906230000},"page":"1081","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights"],"prefix":"10.3390","volume":"24","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\/0000-0002-0335-0036","authenticated-orcid":false,"given":"Bart\u0142omiej","family":"Jefma\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, 53-345 Wroc\u0142aw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6773-6157","authenticated-orcid":false,"given":"Marta","family":"Kusterka-Jefma\u0144ska","sequence":"additional","affiliation":[{"name":"Department of Quality and Environmental Management, Wroclaw University of Economics and Business, 53-345 Wroc\u0142aw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2012.04.038","article-title":"Modeling Uncertainty in Multi-Criteria Decision Analysis","volume":"223","author":"Durbach","year":"2012","journal-title":"Eur. 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