{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:17:55Z","timestamp":1777702675908,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,3,16]],"date-time":"2019-03-16T00:00:00Z","timestamp":1552694400000},"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":[[2019,3,16]]},"abstract":"<jats:p>In this study, we propose a formulation of a Mond-Weir type dual program for a multiobjective nonlinear optimization problem under fuzzy environment. To deal with the multiobjectivity in the formulation, we consider the concept of weak Pareto optimal solution in the fuzzy sense. We use the Hukuhara metric\/ difference to define the distance\/difference between two fuzzy numbers. Further, we establish weak and strong duality theorems under fuzzy pseudo\/quasi-convexity assumptions. Moreover, we also validate these duality relations using various numerical illustrations.<\/jats:p>","DOI":"10.3233\/jifs-171797","type":"journal-article","created":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T17:10:22Z","timestamp":1553015422000},"page":"1361-1373","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A fuzzy multiple objective nonlinear optimization problem and its duality results"],"prefix":"10.1177","volume":"36","author":[{"given":"S. K.","family":"Gupta","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Dangar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Marwari College, Bihar, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Al-Homidan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,3,16]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(70)90078-8"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00938952"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00122-6"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.17.4.B141"},{"key":"e_1_3_2_6_2","author":"Delgado M.","year":"1994","unstructured":"DelgadoM., KacprzykJ., VerdegayJ. L. and VilaM. A., Fuzzy Optimization, Recent Advances, ed., New York, Physica-Verlag (1994).","journal-title":"Recent Advances"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-013-9176-7"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-018-1812-x"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.04.012"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90018-0"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(90)90123-N"},{"key":"e_1_3_2_12_2","first-page":"274","article-title":"Fuzzy multi objective optimization: With reference to multi objective transportation problem","volume":"6","author":"Khan A. J.","year":"2014","unstructured":"KhanA. J. and DasD. K., Fuzzy multi objective optimization: With reference to multi objective transportation problem, Rec. Res. Sci. Tech. 6 (2014), 274\u2013282.","journal-title":"Rec. Res. Sci. Tech."},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57949-3"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-010-9071-4"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1995.1307"},{"key":"e_1_3_2_16_2","first-page":"263","volume-title":"Generalized concavity in optimization and Economics","author":"Mond B.","year":"1999","unstructured":"MondB., WeirT., Generalized concavity and duality, in: SchaibleS. ZiembaW.T. (Eds.), Generalized concavity in optimization and Economics, Academic Press New York (1999), 263\u2013280."},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0141-3"},{"key":"e_1_3_2_18_2","first-page":"415","article-title":"Duality in fuzzy linear programming, University of Texas at Austin","author":"Rodder W.","year":"1977","unstructured":"RodderW. and ZimmermannH. J., Duality in fuzzy linear programming, University of Texas at Austin, Internat. Symp. on Extremal Methods and Systems Analysis (1977), 415\u2013427.","journal-title":"Internat. Symp. on Extremal Methods and Systems Analysis"},{"key":"e_1_3_2_19_2","first-page":"231","article-title":"Duality theory in multiobjective programming","volume":"9","author":"Singh C.","year":"1988","unstructured":"SinghC., Duality theory in multiobjective programming, J. Inform. Optim. Sci. 9 (1988), 231\u2013240.","journal-title":"J. Inform. Optim. Sci."},{"key":"e_1_3_2_20_2","volume-title":"Operations Research and Statistics","author":"Slowinski R.","year":"1998","unstructured":"SlowinskiR., Fuzzy Sets in Decision Analysis, ed., Operations Research and Statistics, Boston, Kluwer Academic Publishers (1998)."},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.06.009"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40535-016-0029-7"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1017\/S000497270000277X"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/135625"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000037411.25509.6a"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-007-9014-x"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2007.08.011"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-009-9061-6"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2004.12.012"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90031-3"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171797","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-171797","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171797","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:36:38Z","timestamp":1777455398000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-171797"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,16]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3,16]]}},"alternative-id":["10.3233\/JIFS-171797"],"URL":"https:\/\/doi.org\/10.3233\/jifs-171797","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,16]]}}}