{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T07:24:32Z","timestamp":1773300272003,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T00:00:00Z","timestamp":1574294400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T00:00:00Z","timestamp":1574294400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s40314-019-1012-4","type":"journal-article","created":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T15:03:31Z","timestamp":1574348611000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Multi-objective non-linear four-valued refined neutrosophic optimization"],"prefix":"10.1007","volume":"39","author":[{"given":"Gul","family":"Freen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sajida","family":"Kousar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumbal","family":"Khalil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,21]]},"reference":[{"issue":"1","key":"1012_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atansassov","year":"1986","unstructured":"Atansassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"1012_CR2","doi-asserted-by":"publisher","first-page":"B-141","DOI":"10.1287\/mnsc.17.4.B141","volume":"17","author":"RE Bellman","year":"1970","unstructured":"Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):B-141","journal-title":"Manag Sci"},{"issue":"3","key":"1012_CR3","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s41872-018-0052-x","volume":"7","author":"SK Bharati","year":"2018","unstructured":"Bharati SK (2018a) Solving optimization problems under hesitant fuzzy environment. Life Cycle Reliab Saf Eng 7(3):127\u2013136","journal-title":"Life Cycle Reliab Saf Eng"},{"key":"1012_CR4","unstructured":"Bharati SK (2018b) Hesitant fuzzy computational algorithm for multiobjective optimization problems. Int J Dyn Control:1\u20138"},{"issue":"1","key":"1012_CR5","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s00500-018-3100-6","volume":"23","author":"SK Bharati","year":"2019","unstructured":"Bharati SK, Singh SR (2019) Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment. Soft Comput 23(1):77\u201384","journal-title":"Soft Comput"},{"issue":"3","key":"1012_CR6","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0165-0114(89)90260-1","volume":"32","author":"L Campos","year":"1989","unstructured":"Campos L (1989) Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets Syst 32(3):275\u2013289","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"1012_CR7","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0165-0114(86)80028-8","volume":"20","author":"C Carlsson","year":"1986","unstructured":"Carlsson C, Korhonen P (1986) A parametric approach to fuzzy linear programming. Fuzzy Sets Syst 20(1):17\u201330","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"1012_CR8","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.ejor.2013.01.046","volume":"228","author":"S Chakrabortty","year":"2013","unstructured":"Chakrabortty S, Pal M, Nayak PK (2013) Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages. Eur J Oper Res 228(2):381\u2013387","journal-title":"Eur J Oper Res"},{"issue":"1\u20133","key":"1012_CR9","first-page":"229","volume":"11","author":"S Chanas","year":"1983","unstructured":"Chanas S (1983) The use of parametric programming in fuzzy linear programming. Fuzzy Sets Syst 11(1\u20133):229\u2013241","journal-title":"Fuzzy Sets Syst"},{"key":"1012_CR10","first-page":"88","volume":"9","author":"P Das","year":"2015","unstructured":"Das P, Roy TK (2015) Multi-objective non-linear programming problem based on neutrosophic optimization technique and its application in riser design problem. Neutrosoph Sets Syst 9:88\u201395","journal-title":"Neutrosoph Sets Syst"},{"key":"1012_CR11","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.ins.2019.06.058","volume":"503","author":"A Ghodousian","year":"2019","unstructured":"Ghodousian A (2019) Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by Dubois-Prade family of t-norms. Inf Sci 503:291\u2013306","journal-title":"Inf Sci"},{"key":"1012_CR12","unstructured":"Guu SM, Wu YK (2018) Multiple objective optimization for systems with addition-min fuzzy relational inequalities. Fuzzy Optim Decis Making:1\u201316"},{"issue":"4","key":"1012_CR13","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1109\/TEVC.2013.2281534","volume":"18","author":"H Jain","year":"2013","unstructured":"Jain H, Deb K (2013) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602\u2013622","journal-title":"IEEE Trans Evol Comput"},{"key":"1012_CR14","doi-asserted-by":"crossref","unstructured":"Kandasamy I, Smarandache F (2016) Triple refined indeterminate neutrosophic sets for personality classification. In: IEEE symposium series on computational intelligence (SSCI), pp 1\u20138","DOI":"10.1109\/SSCI.2016.7850153"},{"issue":"3","key":"1012_CR15","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0165-0114(89)90019-5","volume":"30","author":"MK Luhandjula","year":"1989","unstructured":"Luhandjula MK (1989) Fuzzy optimization: an appraisal. Fuzzy Sets Syst 30(3):257\u2013282","journal-title":"Fuzzy Sets Syst"},{"issue":"6\u20137","key":"1012_CR16","first-page":"971","volume":"28","author":"NV Sahinidis","year":"1983","unstructured":"Sahinidis NV (1983) Optimization under uncertainty: state-of-the-art and opportunities. Comput Chem Eng 28(6\u20137):971\u2013983","journal-title":"Comput Chem Eng"},{"issue":"3","key":"1012_CR17","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/0165-0114(89)90017-1","volume":"30","author":"M Sakawa","year":"1989","unstructured":"Sakawa M, Yano H (1989) An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets Syst 30(3):221\u2013238","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"1012_CR18","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1007\/s40815-017-0362-6","volume":"20","author":"M Sarkar","year":"2018","unstructured":"Sarkar M, Roy TK (2018) Optimization of welded beam structure using neutrosophic optimization technique: a comparative study. Int J Fuzzy Syst 20(3):847\u2013860","journal-title":"Int J Fuzzy Syst"},{"key":"1012_CR19","doi-asserted-by":"crossref","unstructured":"Singh H, Gupta MM, Meitzler T, Hou ZG, Garg KK, Solo AM, Zadeh LA (2013) Real-life applications of fuzzy logic. Adv Fuzzy Syst","DOI":"10.1155\/2013\/581879"},{"key":"1012_CR20","unstructured":"Smarandache F (1999) A unifying field in logics: neutrosophic logic. In: Philosophy. American Research Press, pp 1\u2013141"},{"key":"1012_CR21","unstructured":"Smarandache F (2013) n-valued refined neutrosophic logic and its applications to physics, infinite study"},{"issue":"1","key":"1012_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0165-0114(84)90022-8","volume":"139","author":"HK Tanaka","year":"1984","unstructured":"Tanaka HK, Asai K (1984) Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst 139(1):1\u201310","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"1012_CR23","first-page":"117","volume":"17","author":"J Tang","year":"2004","unstructured":"Tang J, Wang DW, Fung RY, Yung KL (2004) Understanding of fuzzy optimization: theories and methods. J Syst Sci Complex 17(1):117\u2013136","journal-title":"J Syst Sci Complex"},{"issue":"2","key":"1012_CR24","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","volume":"20","author":"IB Turksen","year":"1986","unstructured":"Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20(2):191\u2013210","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"1012_CR25","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0165-0114(84)90096-4","volume":"14","author":"JL Verdegay","year":"1984","unstructured":"Verdegay JL (1984) A dual approach to solve the fuzzy linear programming problem. Fuzzy Sets Syst 14(2):131\u2013141","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"1012_CR26","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/s10700-016-9250-z","volume":"16","author":"SP Wan","year":"2017","unstructured":"Wan SP, Wang F, Xu GL, Dong JY, Tang J (2017) An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations. Fuzzy Optim Decis Making 16(3):269\u2013295","journal-title":"Fuzzy Optim Decis Making"},{"key":"1012_CR27","unstructured":"Wang H, Madiraju P, Zhang Y, Sunderraman R (2004) Interval neutrosophic sets. arXivpreprint arXiv:math\/0409113"},{"key":"1012_CR28","unstructured":"Wang H, Smarandache F, Zhang Y, Sunderraman R: Interval neutrosophic sets. arXivpreprint arXiv:cs\/0410056"},{"issue":"3","key":"1012_CR29","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338\u2013353","journal-title":"Inf Control"},{"issue":"2","key":"1012_CR30","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1515\/jisys-2016-0088","volume":"27","author":"LA Zadeh","year":"2018","unstructured":"Zadeh LA (2018) Double-valued neutrosophic sets, their minimum spanning trees, and clustering algorithm. J Intell Syst 27(2):163\u2013182","journal-title":"J Intell Syst"},{"key":"1012_CR31","unstructured":"Zhou A, Wang Y, Zhang J (2018) Objective extraction via fuzzy clustering in evolutionary many-objective optimization. Inf Sci"},{"issue":"1","key":"1012_CR32","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0165-0114(78)90031-3","volume":"1","author":"HJ Zimmermann","year":"1978","unstructured":"Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45\u201355","journal-title":"Fuzzy Sets Syst"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-1012-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-1012-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-1012-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T03:13:50Z","timestamp":1605842030000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-1012-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,21]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1012"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-1012-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,21]]},"assertion":[{"value":"8 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 November 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"35"}}