{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:20:55Z","timestamp":1773656455171,"version":"3.50.1"},"reference-count":11,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:00:00Z","timestamp":1559088000000},"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":[[2019,6,11]]},"abstract":"<jats:p>Linear regression models with fuzzy independent variables and crisp parameters are considered in this paper. The constant term may be fuzzy. It is determined using calculus of variations. Sometimes linear regression models do not satisfy the conditions under which the least squares estimator should be consistent. It is known from econometrics that in some cases instrumental variables can be used to find a consistent estimator for such models. In this paper, an instrumental variables estimator of a linear fuzzy regression model is constructed and consistency of the estimator is established.<\/jats:p>","DOI":"10.3233\/jifs-181327","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:39:47Z","timestamp":1559302787000},"page":"5457-5462","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Instrumental variables estimation of fuzzy regression models"],"prefix":"10.1177","volume":"36","author":[{"given":"Alexey S.","family":"Shvedov","sequence":"first","affiliation":[{"name":"Department of Applied Economics, National Research University Higher School of Economics, Moscow, Russia"}]}],"member":"179","published-online":{"date-parts":[[2019,5,29]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.04.011"},{"key":"e_1_3_1_3_2","first-page":"63","article-title":"Multiple fuzzy regression model for fuzzy input-output data","volume":"13","author":"Chachi J.","year":"2016","unstructured":"ChachiJ., TaheriS.M., Multiple fuzzy regression model for fuzzy input-output data, Iranian Journal of Fuzzy Systems 13 (2016), 63\u201378.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33517-X_24"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.02.001"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(78)90019-1"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(79)90020-3"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90093-4"},{"key":"e_1_3_1_9_2","first-page":"121","article-title":"Estimating the means and the covariances of fuzzy random variables","volume":"42","author":"Shvedov A.S.","year":"2016","unstructured":"ShvedovA.S., Estimating the means and the covariances of fuzzy random variables, Applied Econometrics 42 (2016), 121\u2013138 (in Russian).","journal-title":"Applied Econometrics"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.04.001"},{"key":"e_1_3_1_11_2","first-page":"328","article-title":"On fuzzy least-squares regression analysis","volume":"18","author":"Veldyaksov V.N.","year":"2014","unstructured":"VeldyaksovV.N., ShvedovA.S., On fuzzy least-squares regression analysis, Ekonomicheskii Zhurnal VSE 18 (2014), 328\u2013344 (in Russian).","journal-title":"Ekonomicheskii Zhurnal VSE"},{"key":"e_1_3_1_12_2","first-page":"508","article-title":"Hypothesis testing in regression models with fuzzy data","volume":"18","author":"Veldyaksov V.N.","year":"2014","unstructured":"VeldyaksovV.N., ShvedovA.S., Hypothesis testing in regression models with fuzzy data, Ekonomicheskii Zhurnal VSE 18 (2014), 508\u2013521 (in Russian).","journal-title":"Ekonomicheskii Zhurnal VSE"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181327","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-181327","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181327","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T19:50:47Z","timestamp":1770234647000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-181327"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,29]]},"references-count":11,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6,11]]}},"alternative-id":["10.3233\/JIFS-181327"],"URL":"https:\/\/doi.org\/10.3233\/jifs-181327","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,29]]}}}