{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:43:56Z","timestamp":1777394636920,"version":"3.51.4"},"publisher-location":"Singapore","reference-count":34,"publisher":"Springer Singapore","isbn-type":[{"value":"9789811315947","type":"print"},{"value":"9789811315954","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T00:00:00Z","timestamp":1540944000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-981-13-1595-4_66","type":"book-chapter","created":{"date-parts":[[2018,10,30]],"date-time":"2018-10-30T17:39:11Z","timestamp":1540921151000},"page":"833-842","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Trapezoidal Intuitionistic Fuzzy Fractional Transportation Problem"],"prefix":"10.1007","author":[{"given":"Shailendra Kumar","family":"Bharati","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,10,31]]},"reference":[{"key":"66_CR1","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1002\/sapm1941201224","volume":"20","author":"FL Hitchcock","year":"1941","unstructured":"Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224\u2013230 (1941)","journal-title":"J. Math. Phys."},{"issue":"5","key":"66_CR2","first-page":"256","volume":"21","author":"K Swarup","year":"1996","unstructured":"Swarup, K.: Transportation technique in linear fractional programming. J. R. Naval Sci. Serv. 21(5), 256\u2013260 (1996)","journal-title":"J. R. Naval Sci. Serv."},{"key":"66_CR3","doi-asserted-by":"crossref","unstructured":"Zadeh, L.A.: Fuzzy Sets. Informat. Control 8, 338\u2013353 (1965)","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"66_CR4","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1287\/mnsc.17.4.B141","volume":"17","author":"RE Bellman","year":"1970","unstructured":"Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag Sci. 17, 141\u2013164 (1970)","journal-title":"Manag Sci."},{"issue":"3","key":"66_CR5","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1007\/s40435-017-0355-1","volume":"6","author":"S. K. Bharati","year":"2017","unstructured":"Bharati, S.K.: Abhishekh, Singh, S.R. Int. J Dynam. Control (2017). https:\/\/doi.org\/10.1007\/s40435-017-0355-1","journal-title":"International Journal of Dynamics and Control"},{"key":"66_CR6","doi-asserted-by":"publisher","first-page":"3629","DOI":"10.1007\/s00500-015-1722-5","volume":"20","author":"Liu Shiang-Tai","year":"2016","unstructured":"Shiang-Tai, Liu: Fractional transporation problem with fuzzy parameters. Soft Comput. 20, 3629\u20133636 (2016)","journal-title":"Soft Comput."},{"key":"66_CR7","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0165-0114(96)00148-0","volume":"91","author":"R Verma","year":"1997","unstructured":"Verma, R., Biswal, M.P., Biswal, A.: Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Sets Syst. 91, 37\u201343 (1997)","journal-title":"Fuzzy Sets Syst."},{"key":"66_CR8","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/S0377-2217(98)00044-7","volume":"117","author":"SK Das","year":"1997","unstructured":"Das, S.K., Goswami, A., Alam, S.S.: Multiobjective transportation problem with interval cost, source and destination parameters. Eur. J. Operation. Res. 117, 100\u2013112 (1997)","journal-title":"Eur. J. Operation. Res."},{"key":"66_CR9","unstructured":"Wahed Abd, F., Waiel, : A multi-objective transportation problem under fuzziness. Fuzzy Sets Syst. 177, 27\u201333 (2001)"},{"key":"66_CR10","first-page":"158","volume":"34","author":"F Wahed Abd","year":"2006","unstructured":"Wahed Abd, F., Waiel, Lee S.M.: A multi-objective transportation problem under fuzziness. Fuzzy Sets Syst. 34, 158\u2013166 (2006)","journal-title":"Fuzzy Sets Syst."},{"key":"66_CR11","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/S0305-0483(03)00054-9","volume":"31","author":"Liu Shiang-Tai","year":"2003","unstructured":"Shiang-Tai, Liu: The total cost bounds of the transportation problem with varying demand and supply. Omega 31, 247\u2013251 (2003)","journal-title":"Omega"},{"key":"66_CR12","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1016\/S0377-2217(02)00731-2","volume":"153","author":"Liu Shiang-Tai","year":"2004","unstructured":"Shiang-Tai, Liu, Kao, Chiang: Solving fuzzy transportation problems based on extension principle. Eur. J. Operatio. Res. 153, 661\u2013674 (2004)","journal-title":"Eur. J. Operatio. Res."},{"key":"66_CR13","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87\u201396 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"66_CR14","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0165-0114(96)00009-7","volume":"86","author":"PP Angelov","year":"1997","unstructured":"Angelov, P.P.: Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst. 86, 299\u2013306 (1997)","journal-title":"Fuzzy Sets Syst."},{"key":"66_CR15","doi-asserted-by":"publisher","unstructured":"Bharati, S.K., Singh, S.R.: Soft Comput (2018). https:\/\/doi.org\/10.1007\/s00500-018-3100-6","DOI":"10.1007\/s00500-018-3100-6"},{"issue":"4","key":"66_CR16","doi-asserted-by":"publisher","first-page":"1799","DOI":"10.1007\/s40435-018-0417-z","volume":"6","author":"Shailendra Kumar Bharati","year":"2018","unstructured":"Bharati, S.K.: Hesitant fuzzy computational algorithm for multiobjective optimization problems. International Journal of Dynamics and Control (2018). https:\/\/doi.org\/10.1007\/s40435-018-0417-z","journal-title":"International Journal of Dynamics and Control"},{"key":"66_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-018-0470-y","author":"SK Bharati","year":"2018","unstructured":"Bharati, S.K., Singh, S.R.: Int. J. Fuzzy Syst. (2018). https:\/\/doi.org\/10.1007\/s40815-018-0470-y","journal-title":"Int. J. Fuzzy Syst."},{"key":"66_CR18","first-page":"305","volume":"11","author":"R Malhotra","year":"2016","unstructured":"Malhotra, R., Bharati, S.K.: Intuitionistic fuzzy two stage multiobjective transportation problems. Advanc. Theor. Appl. Math. 11, 305\u2013316 (2016)","journal-title":"Advanc. Theor. Appl. Math."},{"issue":"23","key":"66_CR19","first-page":"30","volume":"119","author":"SK Bharati","year":"2015","unstructured":"Bharati, S.K., Singh, S.R.: A note on solving a fully intuitionistic fuzzy linear programming problem based on sign distance. Int. J. Comput. Appl. 119(23), 30\u201335 (2015)","journal-title":"Int. J. Comput. Appl."},{"key":"66_CR20","unstructured":"Nishad, A.K., Bharati, S.K., Singh, S.R.: A new centroid method of ranking for intuitionistic fuzzy numbers. In: Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), 28\u201330 Dec, 2012, pp. 151\u2013159. Springer India (2014)"},{"issue":"6","key":"66_CR21","first-page":"17","volume":"89","author":"SK Bharati","year":"2014","unstructured":"Bharati, S.K., Singh, S.R.: Intuitionistic fuzzy optimization technique in agricultural production planning: a small farm holder perspective. Int. J. Comput. Appl. 89(6), 17\u201323 (2014)","journal-title":"Int. J. Comput. Appl."},{"key":"66_CR22","unstructured":"Bharati, S.K., Nishad, A.K., Singh, S.R.: Solution of multi-objective linear programming problems in intuitionistic fuzzy environment. In: Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28\u201330, 2012, pp. 161\u2013171. Springer India"},{"issue":"1","key":"66_CR23","doi-asserted-by":"publisher","first-page":"10","DOI":"10.7763\/IJMO.2014.V4.339","volume":"4","author":"SK Bharati","year":"2014","unstructured":"Bharati, S.K., Singh, S.R.: Solving multi objective linear programming problems using intuitionistic fuzzy optimization method: a comparative study. Int. J. Model. Optimizat. 4(1), 10\u201316 (2014)","journal-title":"Int. J. Model. Optimizat."},{"key":"66_CR24","first-page":"34","volume":"13","author":"B Jana","year":"2007","unstructured":"Jana, B., Roy, T.K.: Multi-objective intuitionistic fuzzy linear programming and its application in transportation model. Notes Intuition. Fuzzy Sets 13, 34\u201351 (2007)","journal-title":"Notes Intuition. Fuzzy Sets"},{"key":"66_CR25","first-page":"590","volume":"03","author":"RJP Atony","year":"2014","unstructured":"Atony, R.J.P., Savarimuthu, S.J., Pathinathan, T.: Method for solving the transporation problem using triangular intutitionistic fuzzy number. Int. J. Comput. Algorithm 03, 590\u2013605 (2014)","journal-title":"Int. J. Comput. Algorithm"},{"issue":"1-2","key":"66_CR26","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10479-014-1724-1","volume":"243","author":"Sujeet Kumar Singh","year":"2014","unstructured":"Singh, S.K., Yadav, S.P.: A new approach for solving intutionistic fuzzy transporation problem of type-2. Ann. Oper. Res. (2014). https:\/\/doi.org\/10.1007\/s10479-014-1724-1","journal-title":"Annals of Operations Research"},{"issue":"113","key":"66_CR27","first-page":"5633","volume":"8","author":"P Pandian","year":"2014","unstructured":"Pandian, P.: Realistic method for solving fully intuitionistic fuzzy transportation problems. Appl. Math. Sci. 8(113), 5633\u20135639 (2014)","journal-title":"Appl. Math. Sci."},{"issue":"3","key":"66_CR28","first-page":"54","volume":"21","author":"PS Kumar","year":"2015","unstructured":"Kumar, P.S., Hussain, R.J.: A method for solving unbalanced intuitionistic fuzzy transportation problems. Notes Intuition. Fuzzy Sets 21(3), 54\u201365 (2015)","journal-title":"Notes Intuition. Fuzzy Sets"},{"key":"66_CR29","first-page":"1","volume":"1","author":"PS Kumar","year":"2015","unstructured":"Kumar, P.S., Hussain, R.J.: Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. Int. J. Syst. Assur. Eng. Manag. 1, 1\u201312 (2015)","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"issue":"Suppl 2","key":"66_CR30","doi-asserted-by":"publisher","first-page":"1442","DOI":"10.1007\/s13198-017-0613-9","volume":"8","author":"SK Bharati","year":"2017","unstructured":"Bharati, S.K., Malhotra, R.: Int. J. Syst. Assur. Eng. Manag. 8(Suppl 2), 1442 (2017). https:\/\/doi.org\/10.1007\/s13198-017-0613-9","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"66_CR31","doi-asserted-by":"crossref","unstructured":"Pradhan, A., Biswal, M.P.: Computational methodology for linear fractional transportation problem. In: Proceedings of the 2015 Winter Simulation Conference, pp. 3158\u20133159. IEEE Press (2015)","DOI":"10.1109\/WSC.2015.7408448"},{"key":"66_CR32","unstructured":"Porchelvi, R.S., Sheela, A.: A linear fractional interval transportation problem with and without budgetary constraints. Intern. J. Fuzzy Math. Arch. 9(2), 165\u2013170 (2015)"},{"key":"66_CR33","doi-asserted-by":"crossref","unstructured":"Kocken, H.G., Emiroglu, I., Guler, C., Tasci, F., Sivri, M.: The fractional transportation problem with interval demand, supply and costs. In: AIP Conference Proceedings, vol. 1557, No. 1, pp. 339\u2013344. AIP (2013)","DOI":"10.1063\/1.4823932"},{"issue":"3\u20134","key":"66_CR34","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(3\u20134), 181\u2013186 (1962)","journal-title":"Naval Res. Logist. Quart."}],"container-title":["Advances in Intelligent Systems and Computing","Soft Computing for Problem Solving"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-13-1595-4_66","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T19:21:59Z","timestamp":1572376919000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-981-13-1595-4_66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,31]]},"ISBN":["9789811315947","9789811315954"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-981-13-1595-4_66","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"value":"2194-5357","type":"print"},{"value":"2194-5365","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,31]]}}}