{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T17:13:29Z","timestamp":1740158009872,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2017,5,3]],"date-time":"2017-05-03T00:00:00Z","timestamp":1493769600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201406840039"],"award-info":[{"award-number":["201406840039"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673011"],"award-info":[{"award-number":["61673011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Ambient Intell Human Comput"],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s12652-017-0500-x","type":"journal-article","created":{"date-parts":[[2017,5,3]],"date-time":"2017-05-03T07:35:56Z","timestamp":1493796956000},"page":"759-768","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pure exchange competitive equilibrium under uncertainty"],"prefix":"10.1007","volume":"8","author":[{"given":"Qiqiong","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanguo","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,3]]},"reference":[{"key":"500_CR1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10898-009-9492-1","volume":"48","author":"G Anello","year":"2010","unstructured":"Anello G, Donato M, Milasi M (2010) A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption. J Glob Optim 48:279\u2013287","journal-title":"J Glob Optim"},{"key":"500_CR2","doi-asserted-by":"crossref","first-page":"265","DOI":"10.2307\/1907353","volume":"22","author":"K Arrow","year":"1954","unstructured":"Arrow K, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica 22:265\u2013290","journal-title":"Econometrica"},{"key":"500_CR3","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511625756","volume-title":"Fixed point theorems with applications to economics and game theory","author":"K Border","year":"1985","unstructured":"Border K (1985) Fixed point theorems with applications to economics and game theory. Cambrige University Press, Cambrige"},{"issue":"4","key":"500_CR4","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s00500-012-0927-0","volume":"17","author":"X Chen","year":"2013","unstructured":"Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597\u2013604","journal-title":"Soft Comput"},{"key":"500_CR5","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1287\/trsc.14.1.42","volume":"14","author":"S Dafermos","year":"1980","unstructured":"Dafermos S (1980) Traffic equilibrium and variational inequalities. Transp Sci 14:42\u201354","journal-title":"Transp Sci"},{"key":"500_CR6","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/BF01585753","volume":"46","author":"S Dafermos","year":"1990","unstructured":"Dafermos S (1990) Exchange price equilibrium and variational inequalities. Mathe Program 46:391\u2013402","journal-title":"Mathe Program"},{"key":"500_CR7","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0167-6377(84)90055-5","volume":"3","author":"S Dafermos","year":"1984","unstructured":"Dafermos S, Nagurney A (1984) A network formulation of market equilibrium problems and variational inequalities. Oper Res Lett 3:247\u2013250","journal-title":"Oper Res Lett"},{"key":"500_CR8","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1057\/jors.2014.115","volume":"66","author":"C Ding","year":"2014","unstructured":"Ding C, Zhu Y (2014) Two empirical uncertain models for project scheduling problem. J Oper Res Soc 66:1471\u20131480","journal-title":"J Oper Res Soc"},{"issue":"3","key":"500_CR9","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1142\/S0218202508002711","volume":"18","author":"M Donato","year":"2008","unstructured":"Donato M, Milasi M, Vitanza C (2008) Quasi-variational inequality approach of a competitive economic equilibrium problem with utility function: existence of equilibrium. Math Mod Methods Appl Sci 18(3):351\u2013367","journal-title":"Math Mod Methods Appl Sci"},{"key":"500_CR10","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10898-007-9199-0","volume":"40","author":"M Donato","year":"2008","unstructured":"Donato M, Milasi M, Vitanza C (2008) An existence result of a quasi-variational inequality associated to an equilibrium problem. J Glob Optim 40:87\u201397","journal-title":"J Glob Optim"},{"key":"500_CR11","first-page":"464","volume":"168","author":"M Donato","year":"2016","unstructured":"Donato M, Milasi M, Vitanza C (2016) On study of an economic equilibrium with variational inequality arguments. J Optim Appl 168:464\u2013660","journal-title":"J Optim Appl"},{"key":"500_CR12","unstructured":"Gabay D, Moulin H (1980) On the uniqueness and stability of Nash equilibria in noncooperative games. In: Benoussan A, Kleindorfer PR, Tapiero CS (eds) Control applied stochastic, of econometrics and mangement science. Series: contributions to economic analysis, 130 . North-Holland, Amsterdam, pp 271\u2013293"},{"key":"500_CR13","doi-asserted-by":"crossref","first-page":"155","DOI":"10.7146\/math.scand.a-10436","volume":"3","author":"D Gale","year":"1955","unstructured":"Gale D (1955) The law of supply and demand. Math Scand 3:155\u2013169","journal-title":"Math Scand"},{"key":"500_CR14","doi-asserted-by":"publisher","unstructured":"Gao J, Yang X, Liu D (2017) Uncertain shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput. doi: 10.1016\/j.asoc.2016.06.018","DOI":"10.1016\/j.asoc.2016.06.018"},{"issue":"4","key":"500_CR15","first-page":"278","volume":"6","author":"X Ge","year":"2012","unstructured":"Ge X, Zhu Y (2012) A necessary condition of optimality for uncertain optimal control problem. Fuzzy Optim Decis Mak 6(4):278\u2013288","journal-title":"Fuzzy Optim Decis Mak"},{"key":"500_CR16","volume-title":"Uncertainty theory","author":"B Liu","year":"2007","unstructured":"Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin","edition":"2"},{"issue":"1","key":"500_CR17","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3\u201310","journal-title":"J Uncertain Syst"},{"key":"500_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-44354-5","volume-title":"Uncertainty theory","author":"B Liu","year":"2015","unstructured":"Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin","edition":"4"},{"issue":"3","key":"500_CR19","first-page":"181","volume":"4","author":"Y Liu","year":"2010","unstructured":"Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181\u2013186","journal-title":"J Uncertain Syst"},{"key":"500_CR20","doi-asserted-by":"crossref","first-page":"147","DOI":"10.2307\/1907539","volume":"22","author":"L McKenzie","year":"1954","unstructured":"McKenzie L (1954) On equilibrium in Grahams model of world trade and other competitive systems. Econometrica 22:147\u2013161","journal-title":"Econometrica"},{"key":"500_CR21","first-page":"679","volume":"57","author":"M Milasi","year":"2013","unstructured":"Milasi M (2013) Existence theorem for a class of generalized quasi-variational inequalities. J Glob Optim 57:679\u2013688","journal-title":"J Glob Optim"},{"key":"500_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-2178-1","volume-title":"Network economics\u2014a variational inequality approach","author":"A Nagurney","year":"1993","unstructured":"Nagurney A (1993) Network economics\u2014a variational inequality approach. Kluwer Academic Publishers, Boston"},{"key":"500_CR23","volume-title":"Convex structures and economic theory: mathematics in science and engineering","author":"H Nikaid\u00f4","year":"1968","unstructured":"Nikaid\u00f4 H (1968) Convex structures and economic theory: mathematics in science and engineering. Academic Press, New York"},{"key":"500_CR24","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/0020-7225(80)90111-1","volume":"18","author":"J Oden","year":"1980","unstructured":"Oden J, Kikuchi N (1980) Recent advances: theory of variational inequalities with applications to problems of flow through porous media. Int J Eng Sci 18:1173\u20131284","journal-title":"Int J Eng Sci"},{"key":"500_CR25","doi-asserted-by":"crossref","first-page":"368","DOI":"10.2307\/1907464","volume":"19","author":"A Wald","year":"1936","unstructured":"Wald A (1936) On some systems of equations of mathematical economic. Econometrica 19:368\u2013403","journal-title":"Econometrica"},{"key":"500_CR26","volume-title":"Elements economique Politique Pure (Elements of Pure Economics)","author":"L Walras","year":"1874","unstructured":"Walras L (1874) Elements economique Politique Pure (Elements of Pure Economics). Corbaz, Lausanne"},{"key":"500_CR27","doi-asserted-by":"crossref","unstructured":"Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1 (article 17)","DOI":"10.1186\/2195-5468-1-17"},{"issue":"4","key":"500_CR28","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1109\/TFUZZ.2015.2486809","volume":"24","author":"X Yang","year":"2016","unstructured":"Yang X, Gao J (2016) Linear quadratic uncertain differential game with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819\u2013826","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"500_CR29","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s10845-014-1010-8","volume":"28","author":"X Yang","year":"2017","unstructured":"Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515\u2013525","journal-title":"J Intell Manuf"},{"key":"500_CR30","doi-asserted-by":"publisher","unstructured":"Yang X, Yao K (2016) Uncertain partial differential equation with application to heat conduction. Fuzzy Optim Decis Mak. doi: 10.1007\/s10700-016-9253-9","DOI":"10.1007\/s10700-016-9253-9"},{"issue":"1","key":"500_CR31","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1142\/S0218488514500056","volume":"22","author":"K Yao","year":"2014","unstructured":"Yao K, Ji X (2014) Uncertain decision making and its application to portfolio selection problem. Int J Uncertain Fuzz and Knowl Based Syst 22(1):113\u2013123","journal-title":"Int J Uncertain Fuzz and Knowl Based Syst"},{"issue":"3","key":"500_CR32","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s10845-014-1013-5","volume":"28","author":"J Zhou","year":"2017","unstructured":"Zhou J, Liu Y, Zhang X, Gu X, Wang D (2017) Uncertain risk aversion. J Intell Manuf 28(3):615\u2013624","journal-title":"J Intell Manuf"},{"issue":"7","key":"500_CR33","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1080\/01969722.2010.511552","volume":"41","author":"Y Zhu","year":"2010","unstructured":"Zhu Y (2010) Uncertain optimal control with application to a portfolio selection model. Cybern Syst Int J 41(7):535\u2013547","journal-title":"Cybern Syst Int J"}],"container-title":["Journal of Ambient Intelligence and Humanized Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12652-017-0500-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12652-017-0500-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12652-017-0500-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T22:27:18Z","timestamp":1719181638000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12652-017-0500-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,3]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["500"],"URL":"https:\/\/doi.org\/10.1007\/s12652-017-0500-x","relation":{},"ISSN":["1868-5137","1868-5145"],"issn-type":[{"type":"print","value":"1868-5137"},{"type":"electronic","value":"1868-5145"}],"subject":[],"published":{"date-parts":[[2017,5,3]]}}}