{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T02:09:23Z","timestamp":1781834963746,"version":"3.54.5"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["113-2221-E-197-022"],"award-info":[{"award-number":["113-2221-E-197-022"]}],"id":[{"id":"10.13039\/100020595","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\/s40815-024-01951-5","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T08:36:23Z","timestamp":1736152583000},"page":"284-296","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Interval Fuzzy c-Bivariate Regression Models with Box\u2013Cox Transformation Clustering Approach for the Interval-Valued Data"],"prefix":"10.1007","volume":"28","author":[{"given":"Jin-Tsong","family":"Jeng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen-Chia","family":"Chuang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tzu-Yun","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"issue":"3","key":"1951_CR1","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1145\/331499.331504","volume":"31","author":"AK Jain","year":"1999","unstructured":"Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264\u2013323 (1999)","journal-title":"ACM Comput. Surv."},{"issue":"3","key":"1951_CR2","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1109\/91.236552","volume":"1","author":"RJ Hathaway","year":"1993","unstructured":"Hathaway, R.J., Bezdek, J.C.: Switching regression models and fuzzy clustering. IEEE Trans. Fuzzy Syst. 1(3), 195\u2013204 (1993)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1951_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/9781119010401","volume-title":"Clustering Methodology for Symbolic Data","author":"L Billard","year":"2019","unstructured":"Billard, L., Diday, E.: Clustering Methodology for Symbolic Data. Wiley, Hoboken (2019)"},{"issue":"4","key":"1951_CR4","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1109\/21.286391","volume":"24","author":"M Ichino","year":"1994","unstructured":"Ichino, M., Yaguchi, H.: Generalized Minkowski metrics for mixed feature type data analysis. IEEE Trans. Syst. Man Cybern. 24(4), 698\u2013708 (1994)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"1951_CR5","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/0167-8655(95)80010-Q","volume":"16","author":"KC Gowda","year":"1995","unstructured":"Gowda, K.C., Ravi, T.R.: Agglomerative clustering of symbolic objects using the concepts of both similarity and dissimilarity. Pattern Recognit. Lett. 16, 647\u2013652 (1995)","journal-title":"Pattern Recognit. Lett."},{"issue":"6","key":"1951_CR6","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1109\/3477.809041","volume":"29","author":"KC Gowda","year":"1999","unstructured":"Gowda, K.C., Ravi, T.R.: Clustering of symbolic objects using gravitational approach. IEEE Trans. Syst. Man Cybern. 29(6), 888\u2013894 (1999)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"1951_CR7","unstructured":"de Carvalho, F.d.A.T., de Souza, R.M.C.R., Bezerra, L.X.T.: A dynamical clustering method for symbolic interval data based on a single adaptive Euclidean distance. In: 2006 Ninth Brazilian Symposium on Neural Networks (SBRN\u201906), Ribeirao Preto, Brazil, 2006, pp. 42\u201347 (2006)"},{"issue":"3","key":"1951_CR8","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.patrec.2005.08.014","volume":"27","author":"FDAT de Carvalho","year":"2006","unstructured":"de Carvalho, F.D.A.T., de Souza, R.M.C.R., Chavent, M., Lechevallier, Y.: Adaptive Hausdorff distances and dynamic clustering of symbolic interval data. Pattern Recognit. Lett. 27(3), 167\u2013179 (2006)","journal-title":"Pattern Recognit. Lett."},{"key":"1951_CR9","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.knosys.2012.01.006","volume":"30","author":"J Pang","year":"2012","unstructured":"Pang, J., Ji, W., Zhou, C., Han, X., Wang, Z.: A fuzzy k-prototype clustering algorithm for mixed numeric and categorical data. Knowl. Based Syst. 30, 129\u2013135 (2012)","journal-title":"Knowl. Based Syst."},{"issue":"9","key":"1951_CR10","doi-asserted-by":"publisher","first-page":"6567","DOI":"10.1016\/j.eswa.2010.02.129","volume":"37","author":"JT Jeng","year":"2010","unstructured":"Jeng, J.T., Chuang, C.C., Tao, C.W.: Interval competitive agglomeration clustering algorithm. Expert Syst. Appl. 37(9), 6567\u20136578 (2010)","journal-title":"Expert Syst. Appl."},{"issue":"6","key":"1951_CR11","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/j.patrec.2006.08.014","volume":"28","author":"FATD Carvalho","year":"2007","unstructured":"Carvalho, F.A.T.D.: Fuzzy $$c$$-means clustering methods for symbolic interval data. Pattern Recognit. Lett. 28(6), 423\u2013437 (2007)","journal-title":"Pattern Recognit. Lett."},{"issue":"3","key":"1951_CR12","first-page":"227","volume":"12","author":"JT Jeng","year":"2010","unstructured":"Jeng, J.T., Chuang, C.C., Tseng, C.C., Juan, C.J.: Robust interval competitive agglomeration clustering algorithm with outliers. Int. J. Fuzzy Syst. 12(3), 227\u2013236 (2010)","journal-title":"Int. J. Fuzzy Syst."},{"key":"1951_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116774","volume":"198","author":"SIR Rodr\u00edguez","year":"2022","unstructured":"Rodr\u00edguez, S.I.R., de Carvalho, F.D.A.T.: Clustering interval-valued data with adaptive Euclidean and City-Block distances. Expert Syst. Appl. 198, 116774 (2022)","journal-title":"Expert Syst. Appl."},{"key":"1951_CR14","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.ins.2020.10.054","volume":"555","author":"FDAT de Carvalho","year":"2021","unstructured":"de Carvalho, F.D.A.T., de Neto, E.A.L., da Silva, K.C.F.: A clusterwise nonlinear regression algorithm for interval-valued data. Inf. Sci. 555, 357\u2013385 (2021)","journal-title":"Inf. Sci."},{"issue":"3","key":"1951_CR15","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1007\/s40815-020-00816-x","volume":"22","author":"CC Chuang","year":"2020","unstructured":"Chuang, C.C., Jeng, J.T., Lin, W.Y., Hsiao, C.C., Tao, C.W.: Interval fuzzy c-regression models with competitive agglomeration for symbolic interval-valued data. Int. J. Fuzzy Syst. 22(3), 891\u2013900 (2020)","journal-title":"Int. J. Fuzzy Syst."},{"issue":"1","key":"1951_CR16","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/TSMCB.2011.2161468","volume":"42","author":"SF Su","year":"2012","unstructured":"Su, S.F., Chuang, C.C., Tao, C.W., Jeng, J.T., Hsiao, C.C.: Radial basis function networks with linear interval regression weights for symbolic interval data. IEEE Trans. Syst. Man Cybern. B 42(1), 69\u201380 (2012)","journal-title":"IEEE Trans. Syst. Man Cybern. B"},{"key":"1951_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/s42952-024-00285-0","author":"L Guan","year":"2024","unstructured":"Guan, L., Li, M.: Interval-valued linear regression model with an asymmetric Laplace distribution. J. Korean Stat. Soc. (2024). https:\/\/doi.org\/10.1007\/s42952-024-00285-0","journal-title":"J. Korean Stat. Soc."},{"issue":"Part C","key":"1951_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.122044","volume":"238","author":"L Kong","year":"2024","unstructured":"Kong, L., Gao, X.: A regularized MM estimate for interval-valued regression. Expert Syst. Appl. 238(Part C), 122044 (2024)","journal-title":"Expert Syst. Appl."},{"key":"1951_CR19","unstructured":"Xu, W.: Symbolic data analysis: interval-valued data regression. Master Thesis, Renmin University of China (2005)"},{"key":"1951_CR20","doi-asserted-by":"crossref","unstructured":"Carvalho, F.A.T.D., Neto, E.A.L., Tenorio, C.P.: A new method to fit a linear regression model for interval-valued data. In: Lecture Notes in Computer Science, KI2004 Advances in Artificial Intelligence, pp. 295\u2013306. Springer, Berlin (2004)","DOI":"10.1007\/978-3-540-30221-6_23"},{"key":"1951_CR21","doi-asserted-by":"crossref","unstructured":"de Neto, E.A.L., de Carvalho, F.D.A.T.: Nonlinear regression model to symbolic interval-valued variables. In: 2008 IEEE International Conference on Systems, Man and Cybernetics, Singapore, 2008, pp. 1247\u20131252 (2008)","DOI":"10.1109\/ICSMC.2008.4811454"},{"key":"1951_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.107396","volume":"235","author":"M Xu","year":"2022","unstructured":"Xu, M., Qin, Z.: A bivariate Bayesian method for interval-valued regression models. Knowl. Based Syst. 235, 107396 (2022)","journal-title":"Knowl. Based Syst."},{"key":"1951_CR23","doi-asserted-by":"publisher","first-page":"1917","DOI":"10.1016\/j.physa.2017.11.108","volume":"492","author":"W Xu","year":"2018","unstructured":"Xu, W., Chen, W., Liang, Y.: Feasibility study on the least square method for fitting non-Gaussian noise data. Physica A 492, 1917\u20131930 (2018)","journal-title":"Physica A"},{"key":"1951_CR24","doi-asserted-by":"crossref","unstructured":"Barbosa, N.M.M., Gomes, J.P.P., Mattos, C.L.C., de Oliveira, D.F.: Linear regression models for interval-valued data using log-transformations. In: Congresso Brasileiro de Intelig\u00eancia Computacional, 2020 (2020)","DOI":"10.21528\/CBIC2019-3"},{"key":"1951_CR25","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s10260-022-00640-7","volume":"32","author":"M Riani","year":"2022","unstructured":"Riani, M., Atkinson, A.C., Corbellini, A.: Automatic robust Box\u2013Cox and extended Yeo\u2013Johnson transformations in regression. Stat. Methods Appl. 32, 75\u2013102 (2022)","journal-title":"Stat. Methods Appl."},{"issue":"1","key":"1951_CR26","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1177\/1536867X1001000108","volume":"10","author":"C Lindsey","year":"2010","unstructured":"Lindsey, C., Sheather, S.: Power transformation via multivariate Box\u2013Cox. Stata J. 10(1), 68\u201381 (2010)","journal-title":"Stata J."},{"issue":"7","key":"1951_CR27","doi-asserted-by":"publisher","first-page":"3513","DOI":"10.1080\/03610918.2020.1714662","volume":"51","author":"U Beyaztas","year":"2020","unstructured":"Beyaztas, U., Shang, H.L., Abdel-Salam, A.-S.G.: Functional linear models for interval-valued data. Commun. Stat. Simul. Comput. 51(7), 3513\u20133532 (2020)","journal-title":"Commun. Stat. Simul. Comput."},{"key":"1951_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.cegh.2022.101043","volume":"15","author":"S Marimuthu","year":"2022","unstructured":"Marimuthu, S., Mani, T., Sudarsanam, T.D., George, S., Jeyaseelan, L.: Preferring Box\u2013Cox transformation, instead of log transformation to convert skewed distribution of outcomes to normal in medical research. Clin. Epidemiol. Glob. Health 15, 101043 (2022)","journal-title":"Clin. Epidemiol. Glob. Health"},{"key":"1951_CR29","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1007\/s10044-016-0538-y","volume":"20","author":"EAL de Neto","year":"2017","unstructured":"de Neto, E.A.L., de Carvalho, F.D.A.T.: Nonlinear regression applied to interval-valued data. Pattern Anal. Appl. 20, 809\u2013824 (2017)","journal-title":"Pattern Anal. Appl."},{"key":"1951_CR30","doi-asserted-by":"crossref","unstructured":"Yang, C.-Y., Jeng, J.-T., Chuang, C.-C., Tao, C.W.: Constructing the linear regression models for the symbolic interval-values data using PSO algorithm. In: International Conference on System Science and Engineering (ICSSE), 2011 (2011)","DOI":"10.1109\/ICSSE.2011.5961895"},{"key":"1951_CR31","doi-asserted-by":"publisher","first-page":"3002","DOI":"10.1016\/j.csda.2006.01.015","volume":"51","author":"M\u00c1 Gil","year":"2007","unstructured":"Gil, M.\u00c1., Gonz\u00e1lez-Rodr\u00edguez, G., Colubi, A., Montenegro, M.: Testing linear independence in linear models with interval-valued data. Comput. Stat. Data Anal. 51, 3002\u20133015 (2007)","journal-title":"Comput. Stat. Data Anal."},{"key":"1951_CR32","unstructured":"Xu, W.: Symbolic data analysis: interval-valued data regression. Doctoral Dissertation, University of Georgia (2010)"},{"issue":"3","key":"1951_CR33","doi-asserted-by":"publisher","first-page":"1500","DOI":"10.1016\/j.csda.2007.04.014","volume":"52","author":"EAL de Neto","year":"2008","unstructured":"de Neto, E.A.L., de Carvalho, F.D.A.T.: Centre and range method for fitting a linear regression model to symbolic interval data. Comput. Stat. Data Anal. 52(3), 1500\u20131515 (2008)","journal-title":"Comput. Stat. Data Anal."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01951-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-024-01951-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-024-01951-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T20:12:24Z","timestamp":1771877544000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-024-01951-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,6]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["1951"],"URL":"https:\/\/doi.org\/10.1007\/s40815-024-01951-5","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,6]]},"assertion":[{"value":"3 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}