{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:14:11Z","timestamp":1648761251012},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Uncert. Sys."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:p> Uncertainty theory has been initiated in 2007 by Liu, as an axiomatically developed notion, which considers the uncertainty on data as a belief degree on the domain expert\u2019s opinion. Uncertain linear optimization is devised to model linear programs in an uncertain environment. In this paper, we investigate the relation between uncertain linear optimization and parametric programming. It is denoted that the problem can be converted to parametric linear optimization problem, at which belief degrees play the role of parameters, and parametric linear optimization with its rich literature provides insightful interpretations. In a point of view, a strictly complementary optimal solution of problem is known for the belief degree [Formula: see text], as well as the associated optimal partition. One may be interested in knowing the region of belief degrees (parameters) where this optimal partition remains invariant for all parameter values (belief degrees) in this region. We consider the linear optimization problem with uncertain rim data, i.e., the right-hand side and the objective function data. The known results in the literature are translated to the language of uncertainty theory, and managerial interpretations are provided. The methodology is illustrated via concrete examples. <\/jats:p>","DOI":"10.1142\/s1752890921500057","type":"journal-article","created":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T16:25:29Z","timestamp":1617639929000},"page":"2150005","source":"Crossref","is-referenced-by-count":0,"title":["Linear Optimization in Uncertain Environment: Sensitivity of the Solution to the Belief Degree"],"prefix":"10.1142","volume":"14","author":[{"given":"Alireza","family":"Ghaffari-Hadigheh","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,4,5]]},"reference":[{"key":"S1752890921500057BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2018.2875692"},{"key":"S1752890921500057BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(83)80083-9"},{"key":"S1752890921500057BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90335-2"},{"key":"S1752890921500057BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.05.033"},{"key":"S1752890921500057BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90184-J"},{"key":"S1752890921500057BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-007-0054-7"},{"key":"S1752890921500057BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S021759591550013X"},{"key":"S1752890921500057BIB008","volume-title":"Approximate Reasoning in Decision analysis","author":"Gupta M. M.","year":"1982"},{"issue":"2","key":"S1752890921500057BIB009","first-page":"94","volume":"2","author":"Ghaffari-Hadigheh A.","year":"2007","journal-title":"Algorithmic Oper. Res."},{"key":"S1752890921500057BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2004.09.058"},{"key":"S1752890921500057BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90018-0"},{"key":"S1752890921500057BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488516500239"},{"key":"S1752890921500057BIB013","series-title":"International Series in Operations Research & Management Science","volume-title":"Stochastic Linear Programming: Models, Theory, and Computation","author":"Kall P.","year":"2010"},{"key":"S1752890921500057BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-31274-3"},{"issue":"2","key":"S1752890921500057BIB015","first-page":"257","volume":"12","author":"Kheirfam B.","year":"2010","journal-title":"Adv. Model. Optimiz."},{"key":"S1752890921500057BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"issue":"1","key":"S1752890921500057BIB017","first-page":"3","volume":"3","author":"Liu B.","year":"2009","journal-title":"J. Uncertain Syst."},{"key":"S1752890921500057BIB018","volume-title":"Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty","volume":"300","author":"Liu B.","year":"2011"},{"key":"S1752890921500057BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.cherd.2016.09.034"},{"key":"S1752890921500057BIB020","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.19980781594"},{"key":"S1752890921500057BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-32698-7_3"},{"key":"S1752890921500057BIB022","doi-asserted-by":"crossref","unstructured":"O. Romanko,  A. G. Hadigheh and  T. Terlaky,  Multiobjective Optimization via Parametric Optimization: Models, Algorithms, and Applications,  Modeling and Optimization: Theory and Applications  (Springer, 2012),  pp. 77\u2013119.","DOI":"10.1007\/978-1-4614-3924-0_5"},{"key":"S1752890921500057BIB023","volume-title":"Interior Point Methods for Linear Optimization","author":"Roos C.","year":"2005"}],"container-title":["Journal of Uncertain Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1752890921500057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T08:10:42Z","timestamp":1617696642000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1752890921500057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":23,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1142\/S1752890921500057"],"URL":"https:\/\/doi.org\/10.1142\/s1752890921500057","relation":{},"ISSN":["1752-8909","1752-8917"],"issn-type":[{"value":"1752-8909","type":"print"},{"value":"1752-8917","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3]]}}}