{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:36:33Z","timestamp":1777703793354,"version":"3.51.4"},"reference-count":47,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T00:00:00Z","timestamp":1456790400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p>In this paper, a new approach is presented to the problem of the clustering regression models with imprecise quantities. In this approach, the response variable and the parameters of model are assumed to be the interval-valued fuzzy numbers. We introduce two indices to investigate the goodness-of-fit of such models based on the similarity measure and the squared errors. In addition to, the predictive ability of the proposed clustering models is evaluated by using the cross-validation method. Finally, the application of the proposed approach in modeling some soil characteristics is studied.<\/jats:p>","DOI":"10.3233\/ifs-152048","type":"journal-article","created":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T10:53:14Z","timestamp":1456829594000},"page":"1339-1351","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Clustering regression based on interval-valued fuzzy outputs and interval-valued fuzzy parameters"],"prefix":"10.1177","volume":"30","author":[{"given":"Mohsen","family":"Arefi","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,3]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"1","article-title":"Estimating the parameters of a fuzzy linear regression model","volume":"5","author":"Arabpour A.R.","year":"2008","unstructured":"ArabpourA.R. and TataM., Estimating the parameters of a fuzzy linear regression model, Iranian Journal of Fuzzy Systems 5 (2008), 1\u201319.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_3_2","first-page":"67","article-title":"Weighted similarity measure on interval-valued fuzzy sets and its application to pattern recognition","volume":"11","author":"Arefi M.","year":"2014","unstructured":"ArefiM. and TaheriS.M., Weighted similarity measure on interval-valued fuzzy sets and its application to pattern recognition, Iranian Journal of Fuzzy Systems 11 (2014), 67\u201379.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2014.2346246"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0950-7051(01)00154-X"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90229-1"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90205-4"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2177271"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00154-9"},{"key":"e_1_3_1_12_2","volume-title":"Proceedings of the 58th World Statistics Congress of the ISI (International Statistical Institute)","author":"Chachi J.","year":"2011","unstructured":"ChachiJ., TaheriS.M., A least-absolutes approach to multiple fuzzy regression, Proceedings of the 58th World Statistics Congress of the ISI (International Statistical Institute), Dublin, Ireland, CPS077-01, 2011."},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2009.2026891"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-007-0198-3"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2006.04.036"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.02.003"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.11.005"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.06.001"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/21.229476"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4467-2"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90006-7"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.08.005"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/949143"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2009.06.009"},{"key":"e_1_3_1_25_2","first-page":"19","article-title":"Fuzzy linear regression model with crisp coefficients: A goal programing approach","volume":"7","author":"Hasanpour H.","year":"2010","unstructured":"HasanpourH., MalekiH.R. and YaghoubiM.A., Fuzzy linear regression model with crisp coefficients: A goal programing approach, Iranian Journal of Fuzzy Systems 7 (2010), 19\u201339.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-010-0688-6"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1328-3"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.04.017"},{"key":"e_1_3_1_29_2","first-page":"649","article-title":"Least absolute deviation estimator in fuzzy regression","volume":"18","author":"Kim K.J.","year":"2005","unstructured":"KimK.J., KimD.H. and ChoiS.H., Least absolute deviation estimator in fuzzy regression, Journal of Applied Mathematics & Computing 18 (2005), 649\u2013656.","journal-title":"Journal of Applied Mathematics & Computing"},{"key":"e_1_3_1_30_2","first-page":"1137","article-title":"A study of cross-validation and bootstrap for accuracy estimation and model selection,pp","volume":"2","author":"Kohavi R.","year":"1995","unstructured":"KohaviR., A study of cross-validation and bootstrap for accuracy estimation and model selection,pp, Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence 2 (1995), 1137\u20131143.","journal-title":"Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2005.04.009"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2002.1184791"},{"key":"e_1_3_1_33_2","first-page":"45","article-title":"Pedomodels fitting with fuzzy least squares regression","volume":"1","author":"Mohammadi J.","year":"2004","unstructured":"MohammadiJ. and TaheriS.M., Pedomodels fitting with fuzzy least squares regression, Iranian Journal of Fuzzy Systems 1 (2004), 45\u201361.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_34_2","first-page":"202","article-title":"Clustering by regression analysis, pp","author":"Motoyoshi M.","year":"2003","unstructured":"MotoyoshiM., MiuraT. and ShioyaI., Clustering by regression analysis, pp, In: Proceedings of Conference on DataWarehousing and Knowledge Discovery (DaWaK) (2003), 202\u2013211.","journal-title":"In: Proceedings of Conference on DataWarehousing and Knowledge Discovery (DaWaK)"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.3103\/S0146411607010026"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9150-9"},{"key":"e_1_3_1_37_2","first-page":"1","article-title":"A fuzzy linear regression model for interval type-2 fuzzy sets","author":"Poleshchuk O.","year":"2012","unstructured":"PoleshchukO. and KomarovE., A fuzzy linear regression model for interval type-2 fuzzy sets, Conference of the North American Fuzzy Information Processing Society (NAFIPS), 2012, pp, 1\u20135.","journal-title":"Conference of the North American Fuzzy Information Processing Society (NAFIPS)"},{"key":"e_1_3_1_38_2","first-page":"1","article-title":"Fuzzy logistic regression: A new possibilistic model and its application in clinical vague status","volume":"8","author":"Pourahmad S.","year":"2011","unstructured":"PourahmadS., AyatollahiS.M.T. and TaheriS.M., Fuzzy logistic regression: A new possibilistic model and its application in clinical vague status, Iranian Journal of Fuzzy Systems 8 (2011), 1\u201317.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_39_2","unstructured":"SambucR. Fonctions \u03c6-floues: Application a I\u2019Aide au Diagnostic en Pathologie Thyroidienne Ph. D. Thesis University of Marseille France 1975."},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00244-9"},{"key":"e_1_3_1_41_2","first-page":"55","article-title":"Fuzzy least absolutes regression, Varna, Bulgaria, 11, pp.\u00a0","author":"Taheri S.M.","year":"2008","unstructured":"TaheriS.M. and KelkinnamaM., Fuzzy least absolutes regression, Varna, Bulgaria, 11, pp.\u00a0, In: Proceding of the Fourth International IEEE Conference on Intelligent Systems (2008), 55\u201358.","journal-title":"In: Proceding of the Fourth International IEEE Conference on Intelligent Systems"},{"key":"e_1_3_1_42_2","first-page":"121","article-title":"Fuzzy linear regression based on least absolute deviations","volume":"9","author":"Taheri S.M.","year":"2012","unstructured":"TaheriS.M. and KelkinnamaM., Fuzzy linear regression based on least absolute deviations, Iranian Journal of Fuzzy Systems 9 (2012), 121\u2013140.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_43_2","first-page":"17","article-title":"Extension principle for vague sets and its applications","volume":"6","author":"Taheri S.M.","year":"2011","unstructured":"TaheriS.M. and ZareiR., Extension principle for vague sets and its applications, Advances in Fuzzy Mathematics 6 (2011), 17\u201326.","journal-title":"Advances in Fuzzy Mathematics"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-30278-7_5"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2005.03.018"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00308-8"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1109\/3477.552181"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00066-5"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-152048","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-152048","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-152048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:36Z","timestamp":1777455576000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-152048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.3233\/IFS-152048"],"URL":"https:\/\/doi.org\/10.3233\/ifs-152048","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}