{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T16:55:46Z","timestamp":1779900946840,"version":"3.53.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2016,6]]},"abstract":"<jats:p> The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches. <\/jats:p>","DOI":"10.1142\/s0218488516500239","type":"journal-article","created":{"date-parts":[[2016,6,13]],"date-time":"2016-06-13T07:39:09Z","timestamp":1465803549000},"page":"451-477","source":"Crossref","is-referenced-by-count":8,"title":["A Parametric Programming Method on Gaussian Type-2 Fuzzy Set and Its Application to a Multilevel Supply Chain"],"prefix":"10.1142","volume":"24","author":[{"given":"Dipak Kumar","family":"Jana","sequence":"first","affiliation":[{"name":"Department of Engineering Science, Haldia Institute of Technology, Haldia, Purba Midna Pur-721657, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sutapa","family":"Pramanik","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manoranjan","family":"Maiti","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2016,6,13]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(84)90057-5"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.03.084"},{"key":"p_4","first-page":"622","volume":"1","author":"Coupland S.","year":"2007","journal-title":"Foundations of Computational Intelligence"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.800692"},{"key":"p_6","first-page":"415","volume":"60","author":"Fegad M. R.","year":"2011","journal-title":"European Journal Scientific Research"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31588-6_78"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008195614074"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1941201224"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800150306"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(01)00069-X"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1109\/ICNN.1995.488968"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.08.005"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.155"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.11.014"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2013.03.020"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.05.015"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.08.031"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.075"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.08.044"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.08.005"},{"key":"p_23","first-page":"1","volume":"1","author":"Miller S.","year":"2012","journal-title":"Australia"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2013.11.004"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.07.012"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488516500239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:03:24Z","timestamp":1565114604000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488516500239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":24,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2016,6,13]]},"published-print":{"date-parts":[[2016,6]]}},"alternative-id":["10.1142\/S0218488516500239"],"URL":"https:\/\/doi.org\/10.1142\/s0218488516500239","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]}}}