{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:25:29Z","timestamp":1777703129067,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2015,8,10]],"date-time":"2015-08-10T00:00:00Z","timestamp":1439164800000},"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":[[2015,8,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, a fixed charge multi-objective solid transportation problem (MOSTP) is formulated and solved. Here, unit transportation costs, fixed charge cost, resources, demands, and capacities of conveyances are considered as random fuzzy in nature. The MOSTP is formulated as a decision making model optimizing possibilistic value at risk by incorporating the concept of value at risk (VaR) into possibility and necessity measure theories. The reduced deterministic constrained problem is solved using generalized reduced gradient (GRG) method (LINGO-14.0). The model is illustrated with numerical examples and some sensitivity analysis.<\/jats:p>","DOI":"10.3233\/ifs-151542","type":"journal-article","created":{"date-parts":[[2015,8,21]],"date-time":"2015-08-21T15:54:44Z","timestamp":1440172484000},"page":"2643-2654","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["A fixed charge multi-objective solid transportation problem in random fuzzy environment"],"prefix":"10.1177","volume":"28","author":[{"given":"Sutapa","family":"Pramanik","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dipak Kumar","family":"Jana","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, Haldia Institute of Technology, Haldia Purba Midna Pur-721657, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoranjan","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,10]]},"reference":[{"key":"e_1_3_1_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1941201224"},{"key":"e_1_3_1_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800150306"},{"key":"e_1_3_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2011.10.014"},{"key":"e_1_3_1_5_1","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1973.10"},{"key":"e_1_3_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(84)90057-5"},{"key":"e_1_3_1_7_1","first-page":"415","article-title":"Finding an optimal solution of transportation problem using interval and triangular membership functions","volume":"60","author":"Fegad MR","year":"2011","unstructured":"FegadMRJadhavAVMinleyAR2011Finding an optimal solution of transportation problem using interval and triangular membership functionsEuropian Journal of Operations Resaerch60415421","journal-title":"Europian Journal of Operations Resaerch"},{"issue":"3","key":"e_1_3_1_8_1","first-page":"541","article-title":"Fuzzy programming algorithm with Linear and Non linear Membership Functions for a StochasticFormulation of The Multiple-objective Transportation problem","volume":"15","author":"Bhattcharya UK","year":"2007","unstructured":"BhattcharyaUK2007Fuzzy programming algorithm with Linear and Non linear Membership Functions for a StochasticFormulation of The Multiple-objective Transportation problemThe Journal of Fuzzy Mathematics153541551","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"e_1_3_1_9_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.26.7.694"},{"issue":"2","key":"e_1_3_1_10_1","first-page":"373","article-title":"Fuzzy programming with hyperbolic membership functions for multi-objective capacitated solid transportation problem","volume":"13","author":"Bit AK","year":"2005","unstructured":"BitAK2005Fuzzy programming with hyperbolic membership functions for multi-objective capacitated solid transportation problemThe Journal of Fuzzy Mathematics132373385","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"e_1_3_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00080-4"},{"key":"e_1_3_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00278-2"},{"key":"e_1_3_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(98)00044-7"},{"key":"e_1_3_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.02.021"},{"key":"e_1_3_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12198-013-0108-0"},{"key":"e_1_3_1_16_1","doi-asserted-by":"publisher","DOI":"10.1504\/IJAOM.2014.059612"},{"issue":"1","key":"e_1_3_1_17_1","first-page":"147","article-title":"Two-phase fuzzy algorithms for multi-objective transportation problem","volume":"12","author":"Gao SP","year":"2004","unstructured":"GaoSPLiuSY2004Two-phase fuzzy algorithms for multi-objective transportation problemThe Journal of Fuzzy Mathematics121147155","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"e_1_3_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00098-2"},{"key":"e_1_3_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00164-4"},{"key":"e_1_3_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90399-3"},{"key":"e_1_3_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(99)00007-6"},{"key":"e_1_3_1_22_1","unstructured":"LiuB2004Uncertainty theoryBerlin\/Heidelberg\/USA New YorkSpringer-Verlag"},{"issue":"1","key":"e_1_3_1_23_1","first-page":"115","article-title":"A Parametric study on transportation problem under fuzzy environment","volume":"11","author":"Saad OM","year":"2003","unstructured":"SaadOMAbassSA2003A Parametric study on transportation problem under fuzzy environmentThe Journal of Fuzzy Mathematics111115124","journal-title":"The Journal of Fuzzy Mathematics"},{"key":"e_1_3_1_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1987.289356"},{"key":"e_1_3_1_25_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-947X(2005)131:6(419)"},{"key":"e_1_3_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90097-3"},{"key":"e_1_3_1_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00148-0"},{"key":"e_1_3_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00155-9"},{"key":"e_1_3_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2012.07.064"},{"key":"e_1_3_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2009.06.016"},{"key":"e_1_3_1_31_1","doi-asserted-by":"crossref","unstructured":"XuJZhouX2011Fuzzy-Like Multiple Objective Decision MakingSpringer","DOI":"10.1007\/978-3-642-18000-2"},{"key":"e_1_3_1_32_1","unstructured":"BirgeJRLouveauxF2011Introduction to stochastic programming2nd edNew York\/Dordrecht\/Heidelberg\/LondonSpringer"},{"key":"e_1_3_1_33_1","unstructured":"InfangerG2011Stochastic programmingNew York\/Dorderecht\/ Heidelberg\/LondonSpringer"},{"key":"e_1_3_1_34_1","first-page":"446","article-title":"The solid transportation problem","volume":"11","author":"Haley KB","year":"1962","unstructured":"HaleyKB1962The solid transportation problemOperations Resesearch11446448257","journal-title":"Operations Resesearch"},{"key":"e_1_3_1_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(99)00007-6"},{"key":"e_1_3_1_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90158-E"},{"key":"e_1_3_1_37_1","unstructured":"SakawaK1993Fuzzy Sets and Interactive Multiobjective OptimizationNew YorkPlenum Press"},{"key":"e_1_3_1_38_1","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141366"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151542","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151542","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151542","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:37:57Z","timestamp":1777455477000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151542"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,10]]},"references-count":37,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,8,10]]}},"alternative-id":["10.3233\/IFS-151542"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151542","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,10]]}}}