{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T05:23:30Z","timestamp":1776057810793,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,2]]},"DOI":"10.1007\/s40747-024-01761-0","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T08:42:18Z","timestamp":1736239338000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["New Jensen\u2013Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS"],"prefix":"10.1007","volume":"11","author":[{"given":"Xinxing","family":"Wu","sequence":"first","affiliation":[]},{"given":"Qian","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Lantian","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4907-3548","authenticated-orcid":false,"given":"Miin-Shen","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Xu","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"issue":"15","key":"1761_CR1","doi-asserted-by":"crossref","first-page":"10335","DOI":"10.1007\/s00500-021-05807-0","volume":"25","author":"C Altan Koyuncu","year":"2021","unstructured":"Altan Koyuncu C, Aydemir E, Ba\u015far\u0131r AC (2021) Selection industry 4.0 maturity model using fuzzy and intuitionistic fuzzy TOPSIS methods for a solar cell manufacturing company. Soft Comput 25(15):10335\u201310349","journal-title":"Soft Comput"},{"key":"1761_CR2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov KT (1986) Intuitionistic fuzzy set. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"1761_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7908-1870-3","volume-title":"Intuitionistic fuzzy sets: theory and applications, studies in fuzziness and soft computing","author":"KT Atanassov","year":"1999","unstructured":"Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications, studies in fuzziness and soft computing, vol 35. Springer-Verlag, Berlin"},{"issue":"3","key":"1761_CR4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0165-0114(96)84611-2","volume":"78","author":"P Burillo","year":"1996","unstructured":"Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78(3):305\u2013316","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"1761_CR5","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1080\/18756891.2016.1204119","volume":"9","author":"G B\u00fcy\u00fck\u00f6zkan","year":"2016","unstructured":"B\u00fcy\u00fck\u00f6zkan G, G\u00fclery\u00fcz S (2016) Multi criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int J Comput Intell Syst 9(4):709\u2013725","journal-title":"Int J Comput Intell Syst"},{"issue":"6","key":"1761_CR6","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1109\/TFUZZ.2015.2421072","volume":"23","author":"ST Chang","year":"2015","unstructured":"Chang ST, Lu KP, Yang MS (2015) Fuzzy change-point algorithms for regression models. IEEE Trans Fuzzy Syst 23(6):2343\u20132357","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1761_CR7","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ins.2016.05.044","volume":"367","author":"SM Chen","year":"2016","unstructured":"Chen SM, Cheng SH, Lan TC (2016) Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367:279\u2013295","journal-title":"Inf Sci"},{"issue":"3","key":"1761_CR8","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1109\/TFUZZ.2017.2738603","volume":"26","author":"S Das","year":"2018","unstructured":"Das S, Guha D, Mesiar R (2018) Information measures in the intuitionistic fuzzy framework and their relationships. IEEE Trans Fuzzy Syst 26(3):1626\u20131637","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1761_CR9","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.knosys.2012.10.006","volume":"39","author":"B Farhadinia","year":"2013","unstructured":"Farhadinia B (2013) A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. Knowl-Based Syst 39:79\u201384","journal-title":"Knowl-Based Syst"},{"issue":"1","key":"1761_CR10","first-page":"30","volume":"3","author":"J Havrda","year":"1967","unstructured":"Havrda J, Charv\u00e1t F (1967) Quantification method of classification processes: concept of structural $$\\alpha $$-entropy. Kybernetika 3(1):30\u201335","journal-title":"Kybernetika"},{"issue":"4","key":"1761_CR11","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1002\/int.20131","volume":"21","author":"WL Hung","year":"2006","unstructured":"Hung WL, Yang MS (2006) Fuzzy entropy on intuitionistic fuzzy sets. Int J Intell Syst 21(4):443\u2013451","journal-title":"Int J Intell Syst"},{"issue":"6","key":"1761_CR12","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1016\/j.ins.2007.11.006","volume":"178","author":"WL Hung","year":"2008","unstructured":"Hung WL, Yang MS (2008) On the $$J$$-divergence of intuitionistic fuzzy sets with its application to pattern recognition. Inf Sci 178(6):1641\u20131650","journal-title":"Inf Sci"},{"key":"1761_CR13","doi-asserted-by":"crossref","unstructured":"Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications a state-of-the-art survey, vol 186. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin","DOI":"10.1007\/978-3-642-48318-9"},{"issue":"3","key":"1761_CR14","first-page":"359","volume":"15","author":"CM Hwang","year":"2013","unstructured":"Hwang CM, Yang MS (2013) New construction for similarity measures between intuitionistic fuzzy sets based on lower, upper and middle fuzzy sets. Int J Fuzzy Syst 15(3):359\u2013366","journal-title":"Int J Fuzzy Syst"},{"key":"1761_CR15","unstructured":"Jafar MN, Saeed M, Haseeb M, et\u00a0al (2021) Matrix Theory for Intuitionistic Fuzzy Hypersoft Sets and its Application in Multi-Attributive Decision-Making Problems. In: Smarandache F, Saeed M, Abdel-Baset M, et\u00a0al (eds) Theory and Application of Hypersoft Set. Pons Publishing House Brussel, chap\u00a04"},{"key":"1761_CR16","doi-asserted-by":"crossref","first-page":"3187","DOI":"10.1109\/ACCESS.2023.3347349","volume":"12","author":"MN Jafar","year":"2024","unstructured":"Jafar MN, Muniba K, Yang MS (2024) Aggregation operators on Pythagorean fuzzy hypersoft matrices with application in the selection of wastewater treatment plants. IEEE Access 12:3187\u20133199","journal-title":"IEEE Access"},{"issue":"7","key":"1761_CR17","first-page":"8","volume":"10","author":"MN Jafar","year":"2024","unstructured":"Jafar MN, Saeed M, Saeed A et al (2024) Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem. Heliyon 10(7):8","journal-title":"Heliyon"},{"issue":"11","key":"1761_CR18","doi-asserted-by":"crossref","first-page":"2216","DOI":"10.1002\/int.22026","volume":"33","author":"R Joshi","year":"2018","unstructured":"Joshi R, Kumar S (2018) A dissimilarity Jensen-Shannon divergence measure for intuitionistic fuzzy sets. Int J Intell Syst 33(11):2216\u20132235","journal-title":"Int J Intell Syst"},{"issue":"3","key":"1761_CR19","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1080\/03081079.2018.1552685","volume":"48","author":"R Joshi","year":"2019","unstructured":"Joshi R, Kumar S (2019) A dissimilarity measure based on Jensen Shannon divergence measure. Int J Gen Syst 48(3):280\u2013301","journal-title":"Int J Gen Syst"},{"issue":"1","key":"1761_CR20","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/18.61115","volume":"37","author":"J Lin","year":"1991","unstructured":"Lin J (1991) Divergence measures based on the Shannon entropy. IEEE Trans Inf Theory 37(1):145\u2013151","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"1761_CR21","doi-asserted-by":"crossref","first-page":"3715","DOI":"10.1109\/TFUZZ.2018.2848245","volume":"26","author":"QD Lohani","year":"2018","unstructured":"Lohani QD, Solanki R, Muhuri PK (2018) Novel adaptive clustering algorithms based on a probabilistic similarity measure over Atanassov intuitionistic fuzzy set. IEEE Trans Fuzzy Syst 26(6):3715\u20133729","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1761_CR22","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cie.2015.12.002","volume":"93","author":"KP Lu","year":"2016","unstructured":"Lu KP, Chang ST, Yang MS (2016) Change-point detection for shifts in control charts using fuzzy shift change-point algorithms. Comput Ind Eng 93:12\u201327","journal-title":"Comput Ind Eng"},{"issue":"2","key":"1761_CR23","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1002\/int.22312","volume":"36","author":"J Mahanta","year":"2021","unstructured":"Mahanta J, Panda S (2021) A novel distance measure for intuitionistic fuzzy sets with diverse applications. Int J Intell Syst 36(2):615\u2013627","journal-title":"Int J Intell Syst"},{"issue":"2","key":"1761_CR24","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/TFUZZ.2014.2315654","volume":"23","author":"I Montes","year":"2015","unstructured":"Montes I, Pal NR, Jani\u0161 V et al (2015) Divergence measures for intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 23(2):444\u2013456","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"2","key":"1761_CR25","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0888-613X(02)00063-4","volume":"30","author":"S Montes","year":"2002","unstructured":"Montes S, Couso I, Gil P et al (2002) Divergence measure between fuzzy sets. Int J Approx Reason 30(2):91\u2013105","journal-title":"Int J Approx Reason"},{"key":"1761_CR26","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1007\/s40747-020-00224-6","volume":"7","author":"M Rahimi","year":"2021","unstructured":"Rahimi M, Kumar P, Moomivand B et al (2021) An intuitionistic fuzzy entropy approach for supplier selection. Complex Intell Syst 7:1869\u20131876","journal-title":"Complex Intell Syst"},{"issue":"3","key":"1761_CR27","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379\u2013423","journal-title":"Bell Syst Tech J"},{"key":"1761_CR28","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ins.2017.10.045","volume":"428","author":"F Shen","year":"2018","unstructured":"Shen F, Ma X, Li Z et al (2018) An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Inf Sci 428:105\u2013119","journal-title":"Inf Sci"},{"issue":"3","key":"1761_CR29","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/S0165-0114(98)00244-9","volume":"114","author":"E Szmidt","year":"2000","unstructured":"Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505\u2013518","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"1761_CR30","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/S0165-0114(98)00402-3","volume":"118","author":"E Szmidt","year":"2001","unstructured":"Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467\u2013477","journal-title":"Fuzzy Sets Syst"},{"key":"1761_CR31","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/978-3-540-73400-0_36","volume-title":"Applications of Fuzzy Sets Theory","author":"E Szmidt","year":"2007","unstructured":"Szmidt E, Kacprzyk J (2007) Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. In: Masulli F, Mitra S, Pasi G (eds) Applications of Fuzzy Sets Theory. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 291\u2013297"},{"issue":"7","key":"1761_CR32","doi-asserted-by":"crossref","first-page":"5791","DOI":"10.1007\/s00500-021-05575-x","volume":"25","author":"NX Thao","year":"2021","unstructured":"Thao NX (2021) Some new entropies and divergence measures of intuitionistic fuzzy sets based on Archimedean t-conorm and application in supplier selection. Soft Comput 25(7):5791\u20135805","journal-title":"Soft Comput"},{"issue":"2","key":"1761_CR33","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.patrec.2006.07.004","volume":"28","author":"IK Vlachos","year":"2007","unstructured":"Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recognit Lett 28(2):197\u2013206","journal-title":"Pattern Recognit Lett"},{"key":"1761_CR34","doi-asserted-by":"crossref","unstructured":"Wang H, Wei G (2008) An effective supplier selection method with intuitionistic fuzzy information. In: Proceedings of the 2008 International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, China, IEEE, pp 1\u20134","DOI":"10.1109\/WiCom.2008.1332"},{"issue":"10","key":"1761_CR35","first-page":"1","volume":"27","author":"X Wu","year":"2017","unstructured":"Wu X, Ding X, Lu T et al (2017) Topological dynamics of Zadeh\u2019s extension on upper semi-continuous fuzzy sets. Int J Bifurc Chaos 27(10):1\u201313","journal-title":"Int J Bifurc Chaos"},{"issue":"5","key":"1761_CR36","doi-asserted-by":"crossref","first-page":"1552","DOI":"10.1109\/TFUZZ.2022.3205435","volume":"31","author":"X Wu","year":"2023","unstructured":"Wu X, Zhu Z, Chen C et al (2023) A monotonous intuitionistic fuzzy TOPSIS method under general linear orders via admissible distance measures. IEEE Trans Fuzzy Syst 31(5):1552\u20131565","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"120","key":"1761_CR37","first-page":"144","volume":"661","author":"X Wu","year":"2024","unstructured":"Wu X, Zhu Z, Chen SM (2024) Strict intuitionistic fuzzy distance\/similarity measures based on Jensen-Shannon divergence. Inf Sci 661(120):144","journal-title":"Inf Sci"},{"issue":"6","key":"1761_CR38","doi-asserted-by":"crossref","first-page":"3980","DOI":"10.1109\/TSMC.2019.2958635","volume":"51","author":"F Xiao","year":"2021","unstructured":"Xiao F (2021) A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans Syst Man Cybern Syst 51(6):3980\u20133992","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"6","key":"1761_CR39","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","volume":"15","author":"Z Xu","year":"2007","unstructured":"Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179\u20131187","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1761_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-29584-3","volume-title":"Intuitionistic fuzzy information aggregation: theory and applications, mathematics monograph series","author":"Z Xu","year":"2012","unstructured":"Xu Z, Cai X (2012) Intuitionistic fuzzy information aggregation: theory and applications, mathematics monograph series, vol 20. Science Press"},{"key":"1761_CR41","first-page":"1","volume":"7849686","author":"MS Yang","year":"2020","unstructured":"Yang MS, Hussian Z (2020) Ali M (2020) Belief and plausibility measures on intuitionistic fuzzy sets with construction of belief-plausibility topsis. Complexity 7849686:1\u201312","journal-title":"Complexity"},{"issue":"1","key":"1761_CR42","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s00607-009-0075-2","volume":"87","author":"J Ye","year":"2010","unstructured":"Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Computing 87(1):55\u201362","journal-title":"Computing"},{"issue":"3","key":"1761_CR43","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338\u2013353","journal-title":"Inf Control"},{"issue":"11","key":"1761_CR44","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1016\/j.fss.2005.11.020","volume":"157","author":"W Zeng","year":"2006","unstructured":"Zeng W, Li H (2006) Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst 157(11):1477\u20131484","journal-title":"Fuzzy Sets Syst"},{"key":"1761_CR45","doi-asserted-by":"crossref","unstructured":"Zhang H (2013) Entropy for intuitionistic fuzzy sets based on distance and intuitionistic index. Int J Uncertain Fuzziness Knowl-Based Syst 21(01):139\u2013155","DOI":"10.1142\/S0218488513500086"},{"key":"1761_CR46","unstructured":"Zhang H (2020) Fuzzy multiple attribute decision making methods and their application. China Economic Publishing House (in Chinese)"},{"issue":"6","key":"1761_CR47","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.knosys.2009.06.007","volume":"22","author":"H Zhang","year":"2009","unstructured":"Zhang H, Zhang W, Mei C (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl-Based Syst 22(6):449\u2013454","journal-title":"Knowl-Based Syst"},{"key":"1761_CR48","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.ins.2020.01.003","volume":"517","author":"L Zhang","year":"2020","unstructured":"Zhang L, Zhan J, Yao Y (2020) Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf Sci 517:315\u2013339","journal-title":"Inf Sci"},{"issue":"21","key":"1761_CR49","doi-asserted-by":"crossref","first-page":"4184","DOI":"10.1016\/j.ins.2008.07.003","volume":"178","author":"QS Zhang","year":"2008","unstructured":"Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its applications. Inf Sci 178(21):4184\u20134191","journal-title":"Inf Sci"},{"key":"1761_CR50","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1007\/s40747-022-00678-w","volume":"8","author":"Z Zhang","year":"2022","unstructured":"Zhang Z, Guo J, Zhang H et al (2022) Product selection based on sentiment analysis of online reviews: an intuitionistic fuzzy TODIM method. Complex Intell Syst 8:3349\u20133362","journal-title":"Complex Intell Syst"}],"container-title":["Complex & Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01761-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-024-01761-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01761-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T16:29:49Z","timestamp":1738945789000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-024-01761-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,7]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["1761"],"URL":"https:\/\/doi.org\/10.1007\/s40747-024-01761-0","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,7]]},"assertion":[{"value":"3 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that there are no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"134"}}