{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T16:54:10Z","timestamp":1769360050578,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T00:00:00Z","timestamp":1681776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T00:00:00Z","timestamp":1681776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s12190-023-01860-0","type":"journal-article","created":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T17:02:33Z","timestamp":1681837353000},"page":"2873-2899","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An efficient fuzzy mathematical approach to solve multi-objective fractional programming problem under fuzzy environment"],"prefix":"10.1007","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7340-9574","authenticated-orcid":false,"given":"Suvasis","family":"Nayak","sequence":"first","affiliation":[]},{"given":"Sujit","family":"Maharana","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"issue":"4","key":"1860_CR1","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s40314-021-01503-9","volume":"40","author":"M Akram","year":"2021","unstructured":"Akram, M., Ullah, I., Allahviranloo, T., Edalatpanah, S.A.: Fully Pythagorean fuzzy linear programming problems with equality constraints. Comp. Appl. Math. 40(4), 120 (2021)","journal-title":"Comp. Appl. Math."},{"issue":"1","key":"1860_CR2","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s40314-021-01756-4","volume":"41","author":"M Akram","year":"2022","unstructured":"Akram, M., Ullah, I., Allahviranloo, T.: A new method for the solution of fully fuzzy linear programming models. Comp. Appl. Math. 41(1), 55 (2022)","journal-title":"Comp. Appl. Math."},{"issue":"1","key":"1860_CR3","first-page":"1975","volume":"41","author":"M Akram","year":"2021","unstructured":"Akram, M., Ullah, I., Allahviranloo, T., Edalatpanah, S.A.: LR-type fully Pythagorean fuzzy linear programming problems with equality constraints. J. Int. Fuzzy Syst. 41(1), 1975\u20131992 (2021)","journal-title":"J. Int. Fuzzy Syst."},{"issue":"6","key":"1860_CR4","first-page":"29","volume":"19","author":"M Akram","year":"2022","unstructured":"Akram, M., Ullah, I., Allahviranloo, T.: A new method to solve linear programming problems in the environment of picture fuzzy sets. Iran J Fuzzy Syst. 19(6), 29\u201349 (2022)","journal-title":"Iran J Fuzzy Syst."},{"issue":"1","key":"1860_CR5","doi-asserted-by":"publisher","first-page":"421","DOI":"10.3233\/JIFS-152087","volume":"32","author":"R Arya","year":"2017","unstructured":"Arya, R., Singh, P.: Fuzzy parametric iterative method for multi-objective linear fractional optimization problems. J. Intell. Fuzzy Syst. 32(1), 421\u2013433 (2017)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"12","key":"1860_CR6","doi-asserted-by":"publisher","first-page":"9105","DOI":"10.1007\/s00500-019-04442-0","volume":"24","author":"R Arya","year":"2020","unstructured":"Arya, R., Singh, P., Kumari, S., Obaidat, M.S.: An approach for solving fully fuzzy multi-objective linear fractional optimization problems. Soft. Comput. 24(12), 9105\u20139119 (2020)","journal-title":"Soft. Comput."},{"issue":"18","key":"1860_CR7","doi-asserted-by":"publisher","first-page":"2701","DOI":"10.1016\/j.fss.2009.02.022","volume":"160","author":"IA Baky","year":"2009","unstructured":"Baky, I.A.: Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy Sets Syst. 160(18), 2701\u20132713 (2009)","journal-title":"Fuzzy Sets Syst."},{"key":"1860_CR8","doi-asserted-by":"crossref","unstructured":"Borza, M., Rambely, A. S.: A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method. J. Int. Fuzzy Syst. pp. 1\u201314 (2022)","DOI":"10.3233\/JIFS-212105"},{"issue":"1","key":"1860_CR9","first-page":"153","volume":"19","author":"M Borza","year":"2022","unstructured":"Borza, M., Rambely, A.S.: An approach based on $$alpha$$-cuts and max-min technique to linear fractional programming with fuzzy coefficients. Iran J. Fuzzy Syst. 19(1), 153\u2013168 (2022)","journal-title":"Iran J. Fuzzy Syst."},{"issue":"3","key":"1860_CR10","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/S0165-0114(01)00060-4","volume":"125","author":"M Chakraborty","year":"2002","unstructured":"Chakraborty, M., Gupta, S.: Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets Syst. 125(3), 335\u2013342 (2002)","journal-title":"Fuzzy Sets Syst."},{"key":"1860_CR11","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1002\/nav.3800090303","volume":"9","author":"A Charnes","year":"1962","unstructured":"Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Naval Res. Logist. Quart. 9, 181\u2013186 (1962)","journal-title":"Naval Res. Logist. Quart."},{"key":"1860_CR12","doi-asserted-by":"publisher","first-page":"6148","DOI":"10.1016\/j.apm.2016.01.044","volume":"40","author":"V Chinnadurai","year":"2016","unstructured":"Chinnadurai, V., Muthukumar, S.: Solving the linear fractional programming problem in a fuzzy environment: Numerical approach. Appl. Math. Model. 40, 6148\u20136164 (2016)","journal-title":"Appl. Math. Model."},{"issue":"3","key":"1860_CR13","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1016\/j.ejor.2005.11.051","volume":"181","author":"JP Costa","year":"2007","unstructured":"Costa, J.P.: Computing non-dominated solutions in MOLFP. Euro. J. Oper. Res. 181(3), 1464\u20131475 (2007)","journal-title":"Euro. J. Oper. Res."},{"issue":"1","key":"1860_CR14","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1051\/ro\/2016022","volume":"51","author":"SK Das","year":"2017","unstructured":"Das, S.K., Mandal, T., Edalatpanah, S.A.: A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Oper. Res. 51(1), 285\u2013297 (2017)","journal-title":"RAIRO-Oper. Res."},{"key":"1860_CR15","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.amc.2013.07.085","volume":"223","author":"OE Emam","year":"2013","unstructured":"Emam, O.E.: Interactive approach to bi-level integer multi-objective fractional programming problem. Appl. Math. Comp. 223, 17\u201324 (2013)","journal-title":"Appl. Math. Comp."},{"issue":"1","key":"1860_CR16","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10700-006-0021-0","volume":"6","author":"A Mehra","year":"2007","unstructured":"Mehra, A., Chandra, S., Bector, C.R.: Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Opt. Dec. Making. 6(1), 5\u201316 (2007)","journal-title":"Fuzzy Opt. Dec. Making."},{"key":"1860_CR17","unstructured":"Miettinen, K.: Nonlinear multiobjective optimization. Springer Science & Business Media (2012)"},{"issue":"1","key":"1860_CR18","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10479-006-7386-x","volume":"143","author":"S Mishra","year":"2006","unstructured":"Mishra, S., Ghosh, A.: Interactive fuzzy programming approach to bi-level quadratic fractional programming problems. Annal Oper. Res. 143(1), 251\u2013263 (2006)","journal-title":"Annal Oper. Res."},{"issue":"2","key":"1860_CR19","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0165-0114(96)00100-5","volume":"89","author":"RH Mohamed","year":"1997","unstructured":"Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst. 89(2), 215\u2013222 (1997)","journal-title":"Fuzzy Sets Syst."},{"issue":"1","key":"1860_CR20","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0377-2217(85)90312-1","volume":"19","author":"I Nykowski","year":"1985","unstructured":"Nykowski, I., Zo\u0142kiewski, Z.: A compromise procedure for the multiple objective linear fractional programming problem. Euro. J. Oper. Res. 19(1), 91\u201397 (1985)","journal-title":"Euro. J. Oper. Res."},{"issue":"2","key":"1860_CR21","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/S0165-0114(02)00374-3","volume":"139","author":"BB Pal","year":"2003","unstructured":"Pal, B.B., Moitra, B.N., Maulik, U.: A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets Syst. 139(2), 395\u2013405 (2003)","journal-title":"Fuzzy Sets Syst."},{"issue":"3","key":"1860_CR22","first-page":"210","volume":"5","author":"A Payan","year":"2014","unstructured":"Payan, A., Noora, A.A.: A linear modelling to solve multi-objective linear fractional programming problem with fuzzy parameters. Int. J. Math. Model. Num. Opt. 5(3), 210\u2013228 (2014)","journal-title":"Int. J. Math. Model. Num. Opt."},{"issue":"1","key":"1860_CR23","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s12190-008-0052-5","volume":"27","author":"B Pop","year":"2008","unstructured":"Pop, B., Stancu-Minasian, I.M.: A method of solving fully fuzzified linear fractional programming problems. J. Appl. Math. Comput. 27(1), 227\u2013242 (2008)","journal-title":"J. Appl. Math. Comput."},{"issue":"11","key":"1860_CR24","first-page":"34","volume":"25","author":"S Pramanik","year":"2011","unstructured":"Pramanik, S., Dey, P.P.: Bi-level linear fractional programming problem based on fuzzy goal programming approach. Int. J. Comput. Appl. 25(11), 34\u201340 (2011)","journal-title":"Int. J. Comput. Appl."},{"issue":"2","key":"1860_CR25","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1016\/j.ejor.2005.08.024","volume":"176","author":"S Pramanik","year":"2007","unstructured":"Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multilevel programming problems. Euro. J. Oper. Res. 176(2), 1151\u20131166 (2007)","journal-title":"Euro. J. Oper. Res."},{"issue":"1","key":"1860_CR26","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/S0165-0114(99)00027-5","volume":"115","author":"M Sakawa","year":"2000","unstructured":"Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Fuzzy Sets Syst. 115(1), 93\u2013103 (2000)","journal-title":"Fuzzy Sets Syst."},{"issue":"1","key":"1860_CR27","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0165-0114(98)00130-4","volume":"109","author":"M Sakawa","year":"2000","unstructured":"Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. Fuzzy Sets Syst. 109(1), 3\u201319 (2000)","journal-title":"Fuzzy Sets Syst."},{"issue":"1","key":"1860_CR28","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1016\/j.aej.2020.10.063","volume":"60","author":"MA El Sayed","year":"2021","unstructured":"El Sayed, M.A., Abo-Sinna, M.A.: A novel approach for fully intuitionistic fuzzy multi-objective fractional transportation problem. Alex. Engin. J. 60(1), 1447\u20131463 (2021)","journal-title":"Alex. Engin. J."},{"issue":"2","key":"1860_CR29","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/S0165-0114(02)00362-7","volume":"136","author":"S Sinha","year":"2003","unstructured":"Sinha, S.: Fuzzy programming approach to multi-level programming problems. Fuzzy Sets Syst. 136(2), 189\u2013202 (2003)","journal-title":"Fuzzy Sets Syst."},{"key":"1860_CR30","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.matpr.2019.04.209","volume":"21","author":"R Srinivasan","year":"2020","unstructured":"Srinivasan, R.: On solving fuzzy linear fractional programming in material aspects. Mater Today Proceed. 21, 155\u2013157 (2020)","journal-title":"Mater Today Proceed."},{"key":"1860_CR31","unstructured":"Stancu-Minasian, I.M.: Fractional Programming: Theory, Methods and Applications. Springer Science & Business Media (2012)"},{"issue":"1","key":"1860_CR32","doi-asserted-by":"publisher","first-page":"41","DOI":"10.2298\/YJOR110522001S","volume":"22","author":"B Stanojevi\u0107","year":"2012","unstructured":"Stanojevi\u0107, B., Stancu-Minasian, I.M.: Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugoslav J. Oper. Res. 22(1), 41\u201350 (2012)","journal-title":"Yugoslav J. Oper. Res."},{"issue":"1","key":"1860_CR33","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1017\/S1446181114000200","volume":"56","author":"SF Tantawy","year":"2014","unstructured":"Tantawy, S.F.: Solving a special class of multiple objective linear fractional programming problems. The ANZ. J. 56(1), 91\u2013103 (2014)","journal-title":"The ANZ. J."},{"issue":"1","key":"1860_CR34","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.apm.2013.05.046","volume":"38","author":"E Valipour","year":"2014","unstructured":"Valipour, E., Yaghoobi, M.A., Mashinchi, M.: An iterative approach to solve multiobjective linear fractional programming problems. Appl. Math. Model. 38(1), 38\u201349 (2014)","journal-title":"Appl. Math. Model."},{"issue":"1","key":"1860_CR35","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1051\/ro\/2013056","volume":"48","author":"C Veeramani","year":"2014","unstructured":"Veeramani, C., Sumathi, M.: Fuzzy mathematical programming approach for solving fuzzy linear fractional programming problem. RAIRO-Oper. Res. 48(1), 109\u2013122 (2014)","journal-title":"RAIRO-Oper. Res."},{"issue":"3","key":"1860_CR36","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.3233\/JIFS-15712","volume":"31","author":"C Veeramani","year":"2016","unstructured":"Veeramani, C., Sumathi, M.: A new method for solving fuzzy linear fractional programming problems. J. Intell. Fuzzy Syst. 31(3), 1831\u20131843 (2016)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"1","key":"1860_CR37","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/0165-0114(78)90031-3","volume":"1","author":"H-J Zimmermann","year":"1978","unstructured":"Zimmermann, H.-J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45\u201355 (1978)","journal-title":"Fuzzy Sets Syst."},{"key":"1860_CR38","unstructured":"Zimmermann, H-J: Fuzzy Set Theory and its Applications. Springer Science & Business Media (2011)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01860-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-023-01860-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-023-01860-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T15:30:31Z","timestamp":1685115031000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-023-01860-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,18]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1860"],"URL":"https:\/\/doi.org\/10.1007\/s12190-023-01860-0","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,18]]},"assertion":[{"value":"16 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2023","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"}}]}}