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In this paper, we change FMOLP\n          problem into the complete stratified fuzzy linear programming problem, then use the\n          stratified simplex method to obtain the fuzzy optimal solution directly without converting\n          them to crisp linear programming problem. We then prove that this fuzzy optimal solution\n          is the fuzzy efficient solution of the original FMOLP problem. A numerical example is\n          given to illustrate the proposed method.<\/jats:p>","DOI":"10.3233\/ifs-151934","type":"journal-article","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T14:25:34Z","timestamp":1449671134000},"page":"2357-2364","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Stratified simplex method for solving fuzzy multi-objective linear          programming problem"],"prefix":"10.1177","volume":"29","author":[{"given":"Qiu-mei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Instituteof Technology,\r          Beijing, P.R. China"},{"name":"School of Science, North China University of Science and Technology, Tangshan, Hebei,\r          P.R.China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu-Gui","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Instituteof Technology,\r          Beijing, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,11,20]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.03.021"},{"key":"e_1_3_1_3_2","unstructured":"Kaufmann A Gupta MM1985Introduction to fuzzy arithmetic: Theory and applicationsVan Nostrand Reinhold 320 New York"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2010.07.037"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9152-7"},{"key":"e_1_3_1_6_2","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.amc.2005.04.106","article-title":"A new approximate algorithm for solving multiple objective linear\n            programming problems with fuzzy parameters","volume":"174","author":"Wu FJ","year":"2006","unstructured":"Wu FJ, Lu J, Zhang GQ2006A new approximate algorithm for solving multiple objective linear programming problems with fuzzy parametersAppl Math Comput174524544","journal-title":"Appl Math Comput"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90031-3"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(84)90022-8"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/01969727308545912"},{"key":"e_1_3_1_10_2","first-page":"213","article-title":"A coordination method for fuzzy multi-objective optimization of system\n            reliability","volume":"16","author":"Huang HZ","year":"2005","unstructured":"Huang HZ, Wu WD, Liu CS2005A coordination method for fuzzy multi-objective optimization of system reliabilityJournal of Intelligent Fuzzy Systems16213220","journal-title":"Journal of Intelligent Fuzzy Systems"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.02.022"},{"key":"e_1_3_1_12_2","first-page":"83","article-title":"On a generalized fuzzy goal optimization for solving fuzzy multi-objective\n            linear programming problems","volume":"18","author":"Lu J","year":"2007","unstructured":"Lu J, Wu FG, Zhang GQ2007On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problemsJournal of Intelligent Fuzzy Systems188397","journal-title":"Journal of Intelligent Fuzzy Systems"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-006-7390-1"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.06.010"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90159-X"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.12.005"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00059-0"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.05.005"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.4.B141"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90097-3"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90223-Q"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90318-X"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151934","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151934","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151934","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:45Z","timestamp":1777455525000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,20]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,11,27]]}},"alternative-id":["10.3233\/IFS-151934"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151934","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,20]]}}}