{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:45:21Z","timestamp":1761597921303,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002398","name":"Sharif University of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002398","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre\u2019s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem.<\/jats:p>","DOI":"10.1155\/2018\/9578270","type":"journal-article","created":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T19:32:17Z","timestamp":1521055937000},"page":"1-7","source":"Crossref","is-referenced-by-count":6,"title":["A Direct Method to Compare Bipolar LR Fuzzy Numbers"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8309-8909","authenticated-orcid":true,"given":"Reza","family":"Ghanbari","sequence":"first","affiliation":[{"name":"Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khatere","family":"Ghorbani-Moghadam","sequence":"additional","affiliation":[{"name":"Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nezam","family":"Mahdavi-Amiri","sequence":"additional","affiliation":[{"name":"Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"2","key":"1","first-page":"767","volume":"10","year":"2014","journal-title":"International Journal of Innovative Computing, Information and Control"},{"issue":"3","key":"2","first-page":"361","volume":"32","year":"2009","journal-title":"Bulletin of the Malaysian Mathematical Sciences Society"},{"key":"3","first-page":"1404","volume":"7","year":"2009","journal-title":"World Applied Sciences Journal"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1207\/s15327957pspr0101_2"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2012.05.003"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1002\/int.20299"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/3477.517031"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.07.037"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.08.022"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.fiae.2015.01.007"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.14317\/jami.2016.049"},{"volume-title":"Monte carlo method in fuzzy optimization","year":"2007","key":"13"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(94)90237-2"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.04.094"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/9578270.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/9578270.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/9578270.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T19:32:20Z","timestamp":1521055940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2018\/9578270\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":14,"alternative-id":["9578270","9578270"],"URL":"https:\/\/doi.org\/10.1155\/2018\/9578270","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"type":"print","value":"1687-7101"},{"type":"electronic","value":"1687-711X"}],"subject":[],"published":{"date-parts":[[2018]]}}}