{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T17:46:14Z","timestamp":1740159974956,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Syst Assur Eng Manag"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s13198-021-01366-7","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T15:57:51Z","timestamp":1634140671000},"page":"1447-1458","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A solution procedure for multi-objective fully quadratic fractional optimization model"],"prefix":"10.1007","volume":"12","author":[{"given":"Namrata","family":"Rani","sequence":"first","affiliation":[]},{"given":"Vandana","family":"Goyal","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9461-8770","authenticated-orcid":false,"given":"Deepak","family":"Gupta","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,13]]},"reference":[{"issue":"2","key":"1366_CR1","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/s12597-019-00368-1","volume":"56","author":"H AbdAlhakim","year":"2019","unstructured":"AbdAlhakim H, Emam O, Abd El-Mageed A (2019) Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem. Opsearch 56(2):367\u2013389","journal-title":"Opsearch"},{"key":"1366_CR2","doi-asserted-by":"publisher","first-page":"012061","DOI":"10.1088\/1742-6596\/1490\/1\/012061","volume":"1490","author":"M Al-Rabeeah","year":"2020","unstructured":"Al-Rabeeah M, Al-Hasani A, Kumar S, Eberhard A (2020) Enhancement of the improved recursive method for multi-objective integer programming problem. J Phys Conf Series 1490:012061","journal-title":"J Phys Conf Series"},{"issue":"2","key":"1366_CR3","doi-asserted-by":"publisher","first-page":"468","DOI":"10.1016\/j.ins.2007.03.029","volume":"178","author":"E Ammar","year":"2008","unstructured":"Ammar E (2008) On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Inf Sci 178(2):468\u2013484","journal-title":"Inf Sci"},{"issue":"2","key":"1366_CR4","first-page":"301","volume":"27","author":"E Ammar","year":"2019","unstructured":"Ammar E, Khalifa H (2019) Solving fully fuzzy multi-objective linear fractional programming problems based on fuzzy programming approach. J Fuzzy Math 27(2):301\u2013312","journal-title":"J Fuzzy Math"},{"issue":"2","key":"1366_CR5","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/s12597-013-0145-2","volume":"51","author":"IA Baky","year":"2014","unstructured":"Baky IA, Eid MH, El Sayed MA (2014) Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm. Opsearch 51(2):280\u2013296","journal-title":"Opsearch"},{"issue":"4","key":"1366_CR6","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1016\/j.asej.2020.03.003","volume":"11","author":"F Farahat","year":"2020","unstructured":"Farahat F et al (2020) Study of achievement stability set for parametric linear fgp problems. Ain Shams Eng J 11(4):1345\u20131353","journal-title":"Ain Shams Eng J"},{"issue":"1","key":"1366_CR7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1093\/imamat\/7.1.76","volume":"7","author":"R Fletcher","year":"1971","unstructured":"Fletcher R (1971) A general quadratic programming algorithm. IMA J Appl Math 7(1):76\u201391","journal-title":"IMA J Appl Math"},{"key":"1366_CR8","doi-asserted-by":"crossref","unstructured":"Goyal V, Rani N, Gupta D (2021) Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming. OPSEARCH pp 1\u201318","DOI":"10.1007\/s12597-021-00545-1"},{"issue":"11","key":"1366_CR9","doi-asserted-by":"publisher","first-page":"2122","DOI":"10.35940\/ijitee.K2011.0981119","volume":"8","author":"D Gupta","year":"2019","unstructured":"Gupta D, Kumar S, Rani N (2019) Fgp in multi-objective non-linear fractional optimization model including triangular fuzzy numbers. Int J Innov Technol Explor Eng 8(11):2122\u20132130","journal-title":"Int J Innov Technol Explor Eng"},{"issue":"2","key":"1366_CR10","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/j.ejor.2007.05.055","volume":"189","author":"N Jozefowiez","year":"2008","unstructured":"Jozefowiez N, Semet F, Talbi EG (2008) Multi-objective vehicle routing problems. Eur J Operation Res 189(2):293\u2013309","journal-title":"Eur J Operation Res"},{"issue":"1","key":"1366_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40819-019-0755-3","volume":"6","author":"B Kaushal","year":"2020","unstructured":"Kaushal B, Arora R, Arora S (2020) An aspect of bilevel fixed charge fractional transportation problem. Int J Appl Comput Math 6(1):1\u201319","journal-title":"Int J Appl Comput Math"},{"issue":"2","key":"1366_CR12","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/s13198-019-00781-1","volume":"10","author":"A Kumar","year":"2019","unstructured":"Kumar A, Pant S, Ram M, Chaube S (2019) Multi-objective grey wolf optimizer approach to the reliability-cost optimization of life support system in space capsule. Int J Syst Assur Eng Manag 10(2):276\u2013284","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"1","key":"1366_CR13","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s13198-019-00941-3","volume":"11","author":"PS Kumar","year":"2020","unstructured":"Kumar PS (2020) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1):189\u2013222","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"1","key":"1366_CR14","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1186\/2251-712X-8-16","volume":"8","author":"K Lachhwani","year":"2012","unstructured":"Lachhwani K, Poonia MP (2012) Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach. J Ind Eng Int 8(1):16","journal-title":"J Ind Eng Int"},{"issue":"3","key":"1366_CR15","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0165-0114(95)00086-0","volume":"77","author":"YJ Lai","year":"1996","unstructured":"Lai YJ (1996) Hierarchical optimization: a satisfactory solution. Fuzzy Sets Syst 77(3):321\u2013335","journal-title":"Fuzzy Sets Syst"},{"issue":"12","key":"1366_CR16","doi-asserted-by":"publisher","first-page":"4179","DOI":"10.1016\/j.apm.2010.04.015","volume":"34","author":"FH Lotfi","year":"2010","unstructured":"Lotfi FH, Noora AA, Jahanshahloo GR, Khodabakhshi M, Payan A (2010) A linear programming approach to test efficiency in multi-objective linear fractional programming problems. Appl Math Modell 34(12):4179\u20134183","journal-title":"Appl Math Modell"},{"issue":"1","key":"1366_CR17","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1007\/s10479-019-03178-2","volume":"296","author":"A Mekhilef","year":"2021","unstructured":"Mekhilef A, Moula\u00ef M, Drici W (2021) Solving multi-objective integer indefinite quadratic fractional programs. Ann Operations Res 296(1):821\u2013840","journal-title":"Ann Operations Res"},{"issue":"2","key":"1366_CR18","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0165-0114(96)00100-5","volume":"89","author":"RH Mohamed","year":"1997","unstructured":"Mohamed RH (1997) The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst 89(2):215\u2013222","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"1366_CR19","first-page":"139","volume":"7","author":"M Osman","year":"2018","unstructured":"Osman M, Emam O, Elsayed M (2018) Interactive approach for multi-level multi-objective fractional programming problems with fuzzy parameters. Beni-Suef Univ J Bas Appl Sci 7(1):139\u2013149","journal-title":"Beni-Suef Univ J Bas Appl Sci"},{"issue":"3","key":"1366_CR20","first-page":"210","volume":"5","author":"A Payan","year":"2014","unstructured":"Payan A, Noora AA (2014) A linear modelling to solve multi-objective linear fractional programming problem with fuzzy parameters. Int J Math Modell Numer Optim 5(3):210\u2013228","journal-title":"Int J Math Modell Numer Optim"},{"issue":"3","key":"1366_CR21","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1504\/IJOR.2019.098310","volume":"34","author":"A Pradhan","year":"2019","unstructured":"Pradhan A, Biswal M (2019) Linear fractional programming problems with some multi-choice parameters. Int J Operation Res 34(3):321\u2013338","journal-title":"Int J Operation Res"},{"issue":"10","key":"1366_CR22","first-page":"13","volume":"30","author":"S Pramanik","year":"2011","unstructured":"Pramanik S, Dey PP (2011) Bi-level multi-objective programming problem with fuzzy parameters. Int J Comput Appl 30(10):13\u201320","journal-title":"Int J Comput Appl"},{"key":"1366_CR23","doi-asserted-by":"crossref","unstructured":"RANI N, GOYAL V, GUPTA D (2020) Fgp approach to bi-level multi-objective quadratic fractional programming with parametric functions","DOI":"10.1007\/s12597-021-00545-1"},{"key":"1366_CR24","doi-asserted-by":"crossref","unstructured":"Rani N, Goyal V, Gupta D (2021) Multi-level multi-objective fully quadratic fractional optimization model with trapezoidal fuzzy numbers using rouben ranking function and fuzzy goal programming. Materials Today: Proceedings","DOI":"10.1016\/j.matpr.2021.01.222"},{"key":"1366_CR25","first-page":"1","volume":"58","author":"RM Rizk-Allah","year":"2020","unstructured":"Rizk-Allah RM, Abo-Sinna MA (2020) A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem. OPSEARCH 58:1\u201329","journal-title":"OPSEARCH"},{"issue":"9","key":"1366_CR26","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1057\/palgrave.jors.2600435","volume":"48","author":"X Shi","year":"1997","unstructured":"Shi X, Xia H (1997) Interactive bilevel multi-objective decision making. J Operation Res Soc 48(9):943\u2013949","journal-title":"J Operation Res Soc"},{"issue":"5\u20136","key":"1366_CR27","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1016\/j.mcm.2007.12.007","volume":"48","author":"S Tantawy","year":"2008","unstructured":"Tantawy S (2008) A new procedure for solving linear fractional programming problems. Math Comput Modell 48(5\u20136):969\u2013973","journal-title":"Math Comput Modell"}],"container-title":["International Journal of System Assurance Engineering and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-021-01366-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13198-021-01366-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-021-01366-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T08:29:53Z","timestamp":1635496193000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13198-021-01366-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,13]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["1366"],"URL":"https:\/\/doi.org\/10.1007\/s13198-021-01366-7","relation":{},"ISSN":["0975-6809","0976-4348"],"issn-type":[{"type":"print","value":"0975-6809"},{"type":"electronic","value":"0976-4348"}],"subject":[],"published":{"date-parts":[[2021,10,13]]},"assertion":[{"value":"3 June 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 October 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The study do not involve any human or animal participations. So, no ethical approval is required. There is no current required as the study do not involve any secondary data and human\/animal participation.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human or animal participations"}}]}}