{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T10:11:33Z","timestamp":1780395093127,"version":"3.54.1"},"reference-count":58,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Atanassov\u2019s intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives\/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives\/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [1]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers.<\/jats:p>","DOI":"10.2478\/jaiscr-2024-0013","type":"journal-article","created":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T14:33:15Z","timestamp":1718116395000},"page":"237-250","source":"Crossref","is-referenced-by-count":4,"title":["Ranking of Alternatives Described by Atanassov\u2019s Intuitionistic Fuzzy Sets \u2013 Reconciling Some Misunderstandings"],"prefix":"10.2478","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2192-6905","authenticated-orcid":false,"given":"Eulalia","family":"Szmidt","sequence":"first","affiliation":[{"name":"Systems Research Institute, Polish Academy of Sciences ul . Newelska 6 , Warsaw , Poland"},{"name":"WIT Academy ul. Newelska 6 , Warsaw , Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4187-5877","authenticated-orcid":false,"given":"Janusz","family":"Kacprzyk","sequence":"additional","affiliation":[{"name":"Systems Research Institute, Polish Academy of Sciences ul . Newelska 6 , Warsaw , Poland"},{"name":"WIT Academy ul. Newelska 6 , Warsaw , Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9215-0046","authenticated-orcid":false,"given":"Pawe\u0142","family":"Bujnowski","sequence":"additional","affiliation":[{"name":"Systems Research Institute, Polish Academy of Sciences ul . Newelska 6 , Warsaw , Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4694-7868","authenticated-orcid":false,"given":"Janusz T.","family":"Starczewski","sequence":"additional","affiliation":[{"name":"Department of Intelligent Computer Systems , Cz\u0119stochowa University of Technology Al . Armii Krajowej 36 , Cz\u0119stochowa , Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2562-236X","authenticated-orcid":false,"given":"Agnieszka","family":"Siwocha","sequence":"additional","affiliation":[{"name":"Information Technology Institute , University of Social Sciences , \u0141\u00f3d\u017a , Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2024,6,11]]},"reference":[{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_001","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, Amount of Information and Its Reliability in the Ranking of Atanassov\u2019s Intuitionistic Fuzzy Alternatives, pp. 7\u201319. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009.","DOI":"10.1007\/978-3-642-02187-9_2"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_002","unstructured":"V. Atanassov, \u201cIntuitionistic fuzzy sets,\u201d in VII ITKR Session, vol. 1697\/84, (Sofia), Central Science-Technological Library of Bulgarian Academy of Sciences, 1983. (in Bulgarian) Reprinted: Int. J. Bioautomation, vol. 20(S1), 2016, pp. S1\u2013S6."},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_003","doi-asserted-by":"crossref","unstructured":"K. T. Atanassov, \u201cIntuitionistic fuzzy sets,\u201d Fuzzy Sets Syst., vol. 20, p. 87\u201396, aug 1986.","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_004","doi-asserted-by":"crossref","unstructured":"K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications. DEU: Physica-Verlag GmbH, 1st ed., 2010.","DOI":"10.1007\/978-3-642-29127-2_1"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_005","doi-asserted-by":"crossref","unstructured":"L. A. Zadeh, \u201cFuzzy sets,\u201d Information and Control, vol. 8, pp. 338\u2013353, 1965.","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_006","doi-asserted-by":"crossref","unstructured":"E. Szmidt, J. Kacprzyk, and P. Bujnowski, \u201cRanking of alternatives described by Atanassov\u2019s intuitionistic fuzzy sets \u2013 a critical review,\u201d in 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1\u20137, 2022.","DOI":"10.1109\/FUZZ-IEEE55066.2022.9882874"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_007","doi-asserted-by":"crossref","unstructured":"K. Atanassov, On Intuitionistic Fuzzy Sets Theory, vol. 283. 01 2012.","DOI":"10.1007\/978-3-642-29127-2"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_008","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. F. Baldwin, \u201cIntuitionistic fuzzy set functions, mass assignment theory, possibility theory and histograms,\u201d 2006 IEEE International Conference on Fuzzy Systems, pp. 35\u201341, 2006.","DOI":"10.1109\/FUZZY.2006.1681691"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_009","unstructured":"E. Szmidt and J. Kacprzyk, \u201cAtanassov\u2019s intuitionistic fuzzy sets demystified,\u201d in Information Processing and Management of Uncertainty in Knowledge-Based Systems (D. Ciucci, I. Couso, J. Medina, D.\u015al\u0119zak, D. Petturiti, B. Bouchon-Meunier, and R. R. Yager, eds.), (Cham), pp. 517\u2013527, Springer International Publishing, 2022."},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_010","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, \u201cTwo and three term representations of intuitionistic fuzzy sets: Some conceptual and analytic aspects,\u201d in 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1\u20138, 2015.","DOI":"10.1109\/FUZZ-IEEE.2015.7338003"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_011","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, A Perspective on Differences Between Atanassov\u2019s Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets, pp. 221\u2013237. Cham: Springer International Publishing, 2017.","DOI":"10.1007\/978-3-319-47557-8_13"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_012","doi-asserted-by":"crossref","unstructured":"E. Szmidt, Distances and Similarities in Intuitionistic Fuzzy Sets, vol. 307 of Studies in Fuzziness and Soft Computing. Springer, 2014.","DOI":"10.1007\/978-3-319-01640-5"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_013","unstructured":"E. Szmidt and J. Kacprzyk, \u201cOn measuring distances between intuitionistic fuzzy sets,\u201d in 1st ICIFS conference, Notes on Intuitionistic Fuzzy Sets, vol. 3, (Sofia), pp. 1\u201313, october 1997."},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_014","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, \u201cDistances between intuitionistic fuzzy sets,\u201d Fuzzy Sets Syst., vol. 114, p. 505\u2013518, sep 2000.","DOI":"10.1016\/S0165-0114(98)00244-9"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_015","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, \u201cEntropy for intuitionistic fuzzy sets,\u201d Fuzzy Sets Syst., vol. 118, p. 467\u2013477, mar 2001.","DOI":"10.1016\/S0165-0114(98)00402-3"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_016","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. 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Pasi, eds.), (Berlin, Heidelberg), pp. 291\u2013297, Springer Berlin Heidelberg, 2007.","DOI":"10.1007\/978-3-540-73400-0_36"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_019","doi-asserted-by":"crossref","unstructured":"E. Szmidt and J. Kacprzyk, \u201cThe Spearman and Kendall rank correlation coefficients between intuitionistic fuzzy sets,\u201d in Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), pp. 521\u2013528, Atlantis Press, 2011\/08.","DOI":"10.2991\/eusflat.2011.85"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_020","doi-asserted-by":"crossref","unstructured":"E. Szmidt, J. Kacprzyk, and P. Bujnowski, \u201cSimilarity measures for Atanassov\u2019s intuitionistic fuzzy sets: some dilemmas and challenges,\u201d Control and Cybernetics, vol. 51, no. 2, pp. 249\u2013266, 2022.","DOI":"10.2478\/candc-2022-0016"},{"key":"2026060209201891083_j_jaiscr-2024-0013_ref_021","unstructured":"H. Bustince, V. Mohedano, E. 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