{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T16:29:06Z","timestamp":1769012946922,"version":"3.49.0"},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.<\/jats:p>","DOI":"10.1155\/2014\/254853","type":"journal-article","created":{"date-parts":[[2014,8,12]],"date-time":"2014-08-12T17:05:50Z","timestamp":1407863150000},"page":"1-22","source":"Crossref","is-referenced-by-count":6,"title":["The Interval-Valued Trapezoidal Approximation of Interval-Valued Fuzzy Numbers and Its Application in Fuzzy Risk Analysis"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5878-1506","authenticated-orcid":true,"given":"Zengtai","family":"Gong","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shexiang","family":"Hai","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"},{"name":"School of Science, Lanzhou University of Technology, Lanzhou 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"21","first-page":"338","volume":"8","year":"1965","journal-title":"Information and Computation"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(86)90077-1"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00368-5"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2008.05.005"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.05.033"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.07.015"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(02)00265-7"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1972.5408553"},{"key":"18","year":"1984"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90029-7"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90093-4"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00277-2"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2004.07.018"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90030-T"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00087-7"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00303-5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2007.06.022"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2008.08.017"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2007.12.037"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2006.11.001"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.02.015"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.02.026"},{"key":"16","series-title":"Princeton Mathematical Series, No. 28","year":"1970"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.08.023"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2012.09.010"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/254853.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/254853.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/254853.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T14:33:06Z","timestamp":1469716386000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/254853\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":25,"alternative-id":["254853","254853"],"URL":"https:\/\/doi.org\/10.1155\/2014\/254853","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}