{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T20:59:52Z","timestamp":1771880392669,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T00:00:00Z","timestamp":1744243200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T00:00:00Z","timestamp":1744243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004772","name":"Natural Science Foundation of Ningxia Province","doi-asserted-by":"publisher","award":["No.2023AAC05046"],"award-info":[{"award-number":["No.2023AAC05046"]}],"id":[{"id":"10.13039\/501100004772","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.62066001"],"award-info":[{"award-number":["No.62066001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ningxia Higher Education First-class Discipline Construction Project","award":["No.NXYLXK2017B09"],"award-info":[{"award-number":["No.NXYLXK2017B09"]}]},{"DOI":"10.13039\/501100012481","name":"Graduate Innovation Project of North Minzu University","doi-asserted-by":"publisher","award":["No.YCX24082"],"award-info":[{"award-number":["No.YCX24082"]}],"id":[{"id":"10.13039\/501100012481","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s40815-024-01954-2","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T19:11:41Z","timestamp":1744225901000},"page":"319-342","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Multi-criteria Decision-Making Method Based on Intuitionistic Fuzzy Entropy and Three-Way Ranking TOPSIS with Applications"],"prefix":"10.1007","volume":"28","author":[{"given":"Changlin","family":"Xu","sequence":"first","affiliation":[]},{"given":"Yushi","family":"Lan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,10]]},"reference":[{"issue":"3","key":"1954_CR1","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338\u2013353 (1965)","journal-title":"Inf. Control"},{"issue":"1","key":"1954_CR2","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov, K.T., Stoeva, S.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87\u201396 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"1954_CR3","doi-asserted-by":"publisher","first-page":"120476","DOI":"10.1016\/j.ins.2024.120476","volume":"667","author":"GF Yu","year":"2024","unstructured":"Yu, G.F., Zuo, W.J.: A novel grade assessment method for cybersecurity situation of online retailing with decision makers\u2019 bounded rationality. Inf. Sci. 667, 120476 (2024)","journal-title":"Inf. Sci."},{"issue":"8","key":"1954_CR4","doi-asserted-by":"publisher","first-page":"3626","DOI":"10.1007\/s40815-022-01350-8","volume":"24","author":"B Ning","year":"2022","unstructured":"Ning, B., Lei, F., Wei, G.: Codas method for multi-attribute decision-making based on some novel distance and entropy measures under probabilistic dual hesitant fuzzy sets. Int. J. Fuzzy Syst. 24(8), 3626\u20133649 (2022)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1954_CR5","doi-asserted-by":"publisher","first-page":"120144","DOI":"10.1016\/j.ins.2024.120144","volume":"661","author":"XX Wu","year":"2024","unstructured":"Wu, X.X., Zhu, Z.Y., Chen, S.-M.: Strict intuitionistic fuzzy distance\/similarity measures based on Jensen-Shannon divergence. Inf. Sci. 661, 120144 (2024)","journal-title":"Inf. Sci."},{"key":"1954_CR6","doi-asserted-by":"publisher","first-page":"119811","DOI":"10.1016\/j.ins.2023.119811","volume":"653","author":"JR Jebadass","year":"2024","unstructured":"Jebadass, J.R., Balasubramaniam, P.: Color image enhancement technique based on interval-valued intuitionistic fuzzy set. Inf. Sci. 653, 119811 (2024)","journal-title":"Inf. Sci."},{"issue":"2","key":"1954_CR7","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1007\/s40815-017-0348-4","volume":"20","author":"MD Ansari","year":"2018","unstructured":"Ansari, M.D., Mishra, A.R., Ansari, F.T.: New divergence and entropy measures for intuitionistic fuzzy sets on edge detection. Int. J. Fuzzy Syst. 20(2), 474\u2013487 (2018)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1954_CR8","doi-asserted-by":"publisher","first-page":"121491","DOI":"10.1016\/j.eswa.2023.121491","volume":"237","author":"A Patel","year":"2024","unstructured":"Patel, A., Jana, S., Mahanta, J.: Construction of similarity measure for intuitionistic fuzzy sets and its application in face recognition and software quality evaluation. Expert Syst. Appl. 237, 121491 (2024)","journal-title":"Expert Syst. Appl."},{"key":"1954_CR9","doi-asserted-by":"publisher","first-page":"103459","DOI":"10.1016\/j.advengsoft.2023.103459","volume":"180","author":"JL Jin","year":"2023","unstructured":"Jin, J.L., Garg, H.: Intuitionistic fuzzy three-way ranking-based topsis approach with a novel entropy measure and its application to medical treatment selection. Adv. Eng. Softw. 180, 103459 (2023)","journal-title":"Adv. Eng. Softw."},{"key":"1954_CR10","doi-asserted-by":"publisher","first-page":"110521","DOI":"10.1016\/j.asoc.2023.110521","volume":"144","author":"A Patel","year":"2023","unstructured":"Patel, A., Jana, S., Mahanta, J.: Intuitionistic fuzzy EM-SWARA-TOPSIS approach based on new distance measure to assess the medical waste treatment techniques. Appl. Soft Comput. 144, 110521 (2023)","journal-title":"Appl. Soft Comput."},{"issue":"1","key":"1954_CR11","doi-asserted-by":"publisher","first-page":"13104","DOI":"10.1111\/exsy.13104","volume":"40","author":"S G\u00fcl","year":"2023","unstructured":"G\u00fcl, S., Aydo\u011fdu, A.: Novel distance and entropy definitions for linear diophantine fuzzy sets and an extension of TOPSIS (LDF-TOPSIS). Expert Syst. 40(1), 13104 (2023)","journal-title":"Expert Syst."},{"issue":"8","key":"1954_CR12","doi-asserted-by":"publisher","first-page":"2532","DOI":"10.1109\/TFUZZ.2022.3228332","volume":"31","author":"Q Lin","year":"2023","unstructured":"Lin, Q., Chen, X., Chen, C., Garibaldi, J.M.: A novel quality control algorithm for medical image segmentation based on fuzzy uncertainty. IEEE Trans. Fuzzy Syst. 31(8), 2532\u20132544 (2023)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"5","key":"1954_CR13","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1007\/s40815-024-01689-0","volume":"26","author":"Y Liu","year":"2024","unstructured":"Liu, Y., Wang, M., Wang, Y.: Location decision of emergency medical supply distribution centers under uncertain environment. Int. J. Fuzzy Syst. 26(5), 1567\u20131603 (2024)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1954_CR14","doi-asserted-by":"crossref","unstructured":"Zhang, J., Lin, J., Wu, T.: An interval intuitionistic fuzzy characterization method based on heterogeneous big data and its application in forest land quality assessment. Int. J. Fuzzy Syst (2024)","DOI":"10.1007\/s40815-024-01765-5"},{"issue":"3","key":"1954_CR15","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.ins.2009.09.021","volume":"180","author":"YY Yao","year":"2010","unstructured":"Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341\u2013353 (2010)","journal-title":"Inf. Sci."},{"key":"1954_CR16","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.ins.2021.03.039","volume":"568","author":"K Zhang","year":"2021","unstructured":"Zhang, K., Dai, J., Zhan, J.: A new classification and ranking decision method based on three-way decision theory and TOPSIS models. Inf. Sci. 568, 54\u201385 (2021)","journal-title":"Inf. Sci."},{"key":"1954_CR17","doi-asserted-by":"publisher","first-page":"119339","DOI":"10.1016\/j.ins.2023.119339","volume":"645","author":"J Tang","year":"2023","unstructured":"Tang, J., Zhang, K.: Three-way decision for three-stage ranking pattern with criterion fuzzy concept. Inf. Sci. 645, 119339 (2023)","journal-title":"Inf. Sci."},{"key":"1954_CR18","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/978-3-030-87334-9_25","volume-title":"Rough Sets","author":"YY Yao","year":"2021","unstructured":"Yao, Y.Y., Shi, C.J.: 3rd: A multi-criteria decision-making method based on three-way rankings. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds.) Rough Sets, vol. 12872, pp. 294\u2013309. Springer, Cham (2021)"},{"issue":"9","key":"1954_CR19","doi-asserted-by":"publisher","first-page":"3841","DOI":"10.1109\/TFUZZ.2021.3131380","volume":"30","author":"K Zhang","year":"2022","unstructured":"Zhang, K., Dai, J., Xu, Z.: The criterion-oriented three-way ranking and clustering strategies in fuzzy decision environments. IEEE Trans. Fuzzy Syst. 30(9), 3841\u20133856 (2022)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"3","key":"1954_CR20","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/0165-0114(96)84611-2","volume":"78","author":"P Burillo","year":"1996","unstructured":"Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78(3), 305\u2013316 (1996)","journal-title":"Fuzzy Sets Syst."},{"issue":"3","key":"1954_CR21","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/S0165-0114(98)00402-3","volume":"118","author":"E Szmidt","year":"2001","unstructured":"Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118(3), 467\u2013477 (2001)","journal-title":"Fuzzy Sets Syst."},{"issue":"23","key":"1954_CR22","first-page":"48","volume":"49","author":"T Wu","year":"2013","unstructured":"Wu, T., Bai, L.H., Liu, E.B., Sun, X.H.: New entropy formula of intuitionistic fuzzy sets and its application. Comput. Eng. Appl. 49(23), 48\u201351 (2013)","journal-title":"Comput. Eng. Appl."},{"issue":"11","key":"1954_CR23","doi-asserted-by":"publisher","first-page":"1477","DOI":"10.1016\/j.fss.2005.11.020","volume":"157","author":"WY Zeng","year":"2006","unstructured":"Zeng, W.Y., Li, H.X.: Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst. 157(11), 1477\u20131484 (2006)","journal-title":"Fuzzy Sets Syst."},{"issue":"01","key":"1954_CR24","first-page":"49","volume":"37","author":"XZ Xu","year":"2023","unstructured":"Xu, X.Z., Li, M.: Arctangent entropy on intuitionistic fuzzy sets with application to multi-attribute decision. Fuzzy Syst. Math. 37(01), 49\u201357 (2023)","journal-title":"Fuzzy Syst. Math."},{"issue":"04","key":"1954_CR25","first-page":"571","volume":"27","author":"CP Wei","year":"2012","unstructured":"Wei, C.P., Gao, Z.H., Guo, T.T.: An intuitionistic fuzzy entropy measure based on trigonometric function. Control Decis. 27(04), 571\u2013574 (2012)","journal-title":"Control Decis."},{"issue":"11","key":"1954_CR26","first-page":"2909","volume":"35","author":"MF Liu","year":"2015","unstructured":"Liu, M.F., Ren, H.P.: A study of multi-attribute decision making based on a new intuitionistic fuzzy entropy measure. Syst. Eng. Theory Pract. 35(11), 2909\u20132916 (2015)","journal-title":"Syst. Eng. Theory Pract."},{"key":"1954_CR27","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1016\/j.cie.2019.06.031","volume":"135","author":"JH Yuan","year":"2019","unstructured":"Yuan, J.H., Luo, X.G.: Approach for multi-attribute decision making based on novel intuitionistic fuzzy entropy and evidential reasoning. Comput. Ind. Eng. 135, 643\u2013654 (2019)","journal-title":"Comput. Ind. Eng."},{"issue":"4","key":"1954_CR28","doi-asserted-by":"publisher","first-page":"549","DOI":"10.3390\/math10040549","volume":"10","author":"LH Zeng","year":"2022","unstructured":"Zeng, L.H., Ren, H.P., Yang, T.H., Xiong, N.: An intelligent expert combination weighting scheme for group decision making in railway reconstruction. Mathematics 10(4), 549 (2022)","journal-title":"Mathematics"},{"issue":"01","key":"1954_CR29","first-page":"265","volume":"38","author":"YH He","year":"2023","unstructured":"He, Y.H., Huang, Y.L., Xiong, S.H.: An evaluation model of airport fire station site selection based on entropy weight intuitionistic fuzzy extended multimoora. Control Decis. 38(01), 265\u2013273 (2023)","journal-title":"Control Decis."},{"issue":"03","key":"1954_CR30","first-page":"470","volume":"29","author":"MM Gao","year":"2014","unstructured":"Gao, M.M., Sun, T., Zhu, J.J.: Revised axiomatic definition and structural formula of intuitionistic fuzzy entropy. Control Decis. 29(03), 470\u2013474 (2014)","journal-title":"Control Decis."},{"key":"1954_CR31","doi-asserted-by":"publisher","first-page":"105372","DOI":"10.1016\/j.engappai.2022.105372","volume":"116","author":"YP Gao","year":"2022","unstructured":"Gao, Y.P., Bao, R.X., Pan, Z., Ma, G.Y., Li, J., Cai, X.Q., Peng, Q.Q.: Mechanical equipment health management method based on improved intuitionistic fuzzy entropy and case reasoning technology. Eng. Appl. Artif. Intell. 116, 105372 (2022)","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"4","key":"1954_CR32","doi-asserted-by":"publisher","first-page":"335","DOI":"10.3390\/axioms10040335","volume":"10","author":"P Thakur","year":"2021","unstructured":"Thakur, P., Kizielewicz, B., Gandotra, N., Shekhovtsov, A., Saini, N., Saeid, A.B., Sa\u0142abun, W.: A new entropy measurement for the analysis of uncertain data in mcda problems using intuitionistic fuzzy sets and copras method. Axioms 10(4), 335 (2021)","journal-title":"Axioms"},{"issue":"6 SI","key":"1954_CR33","doi-asserted-by":"publisher","first-page":"2295","DOI":"10.1007\/s40815-023-01503-3","volume":"25","author":"J Xie","year":"2023","unstructured":"Xie, J., Xu, X., Li, F.: Novel intuitionistic fuzzy distance based on tendency and its application in emergency decision-making. Int. J. Fuzzy Syst. 25(6 SI), 2295\u20132311 (2023)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1954_CR34","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.knosys.2013.04.011","volume":"48","author":"JJ Mao","year":"2013","unstructured":"Mao, J.J., Yao, D.B., Wang, C.C.: A novel cross-entropy and entropy measures of IFSs and their applications. Knowl.-Based Syst. 48, 37\u201345 (2013)","journal-title":"Knowl.-Based Syst."},{"key":"1954_CR35","first-page":"1694","volume":"27","author":"JQ Wang","year":"2012","unstructured":"Wang, J.Q., Wang, P.: Intutionistic linguistic fuzzy multi-criteria decision-making method based on intutionistic fuzzy entropy. Control Decis. 27, 1694\u20131698 (2012)","journal-title":"Control Decis."},{"key":"1954_CR36","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00122574","volume":"5","author":"A Tversky","year":"1992","unstructured":"Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5, 297\u2013323 (1992)","journal-title":"J. Risk Uncertain."},{"key":"1954_CR37","doi-asserted-by":"crossref","unstructured":"Hwang, C.-L., Yoon, K.: Methods for multiple attribute decision making. In: Multiple Attribute Decision Making: Methods and Applications a State-of-the-Art Survey, pp. 58\u2013191 (1981)","DOI":"10.1007\/978-3-642-48318-9_3"},{"key":"1954_CR38","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.ins.2020.01.003","volume":"517","author":"L Zhang","year":"2020","unstructured":"Zhang, L., Zhan, J.M., Yao, Y.Y.: Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf. Sci. 517, 315\u2013339 (2020)","journal-title":"Inf. Sci."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01954-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-024-01954-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01954-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T20:12:34Z","timestamp":1771877554000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-024-01954-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,10]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["1954"],"URL":"https:\/\/doi.org\/10.1007\/s40815-024-01954-2","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,10]]},"assertion":[{"value":"20 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest pertaining to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}