{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T13:08:27Z","timestamp":1773407307919,"version":"3.50.1"},"reference-count":27,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Fuzzy Sets and Systems"],"published-print":{"date-parts":[[2003,5]]},"DOI":"10.1016\/s0165-0114(02)00145-8","type":"journal-article","created":{"date-parts":[[2003,4,4]],"date-time":"2003-04-04T20:00:31Z","timestamp":1049486431000},"page":"391-399","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":25,"title":["A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric"],"prefix":"10.1016","volume":"135","author":[{"given":"Shoumei","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yukio","family":"Ogura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0165-0114(02)00145-8_BIB1","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1214\/aop\/1176996275","article-title":"A strong law of large numbers for random compact sets","volume":"3","author":"Artstein","year":"1975","journal-title":"Ann. Probab."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-247X(65)90049-1","article-title":"Integrals of set-valued functions","volume":"12","author":"Aumann","year":"1965","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB3","series-title":"Topologies on Closed and Closed Convex Sets, Mathematics and Its Applications","author":"Beer","year":"1993"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.7146\/math.scand.a-10868","article-title":"Martingale convergence and the Radon\u2013Nikodym theorem in Banach spaces","volume":"22","author":"Chatterji","year":"1968","journal-title":"Math. Scand."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB5","series-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability II, Part I","first-page":"351","article-title":"Integration of correspondences","author":"Debreu","year":"1966"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB6","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0165-0114(89)90045-6","article-title":"Characterization of compact subsets of fuzzy sets","volume":"29","author":"Diamond","year":"1989","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB7","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0047-259X(91)90012-Q","article-title":"On multivalued martingales whose values may be unbounded","volume":"39","author":"Hess","year":"1991","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB8","series-title":"Multifunctions and Integrands","first-page":"160","article-title":"Strong laws of large numbers for multivalued random variables","volume":"Vol. 1091","author":"Hiai","year":"1984"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB9","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0047-259X(77)90037-9","article-title":"Integrals, conditional expectations and martingales of multivalued functions","volume":"7","author":"Hiai","year":"1977","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB10","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF02589354","article-title":"Sur les fonction d'appui des ensembles convexes dans une espace localement convexe","volume":"3","author":"H\u00f6rmander","year":"1954","journal-title":"Ark. f\u00f6r Mat."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB11","series-title":"Theory of Correspondences Including Applications to Mathematical Economics","author":"Klein","year":"1984"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB12","first-page":"171","article-title":"Limit theorems for fuzzy random variables","volume":"407","author":"Klement","year":"1986","journal-title":"Proc. Roy. Soc. London"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB13","first-page":"905","article-title":"Fuzzy random variables, conditional expectations and fuzzy martingales","volume":"4","author":"Li","year":"1996","journal-title":"J. Fuzzy Math."},{"issue":"3","key":"10.1016\/S0165-0114(02)00145-8_BIB14","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1214\/aop\/1022855757","article-title":"Convergence of set-valued sub- and super-martingales in the Kuratowski\u2013Mosco sense","volume":"26","author":"Li","year":"1998","journal-title":"Ann. Probab."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB15","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/S0165-0114(97)00092-4","article-title":"Convergence of set-valued and fuzzy-valued martingales","volume":"101","author":"Li","year":"1999","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB16","doi-asserted-by":"crossref","unstructured":"S. Li, Y. Ogura, Convergence in graph for fuzzy-valued martingales and smartingales, in: C. Bertoluzza, A.M. Gil, D.A. Ralescu (Eds.), Statistical Modeling, Analysis, and Management of Fuzzy Data, 2002, pp. 72\u201389.","DOI":"10.1007\/978-3-7908-1800-0_5"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB17","series-title":"Limit Theorems and Applications of Set Valued and Fuzzy Valued Random Variables","author":"Li","year":"2002"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB18","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0020-0255(01)00074-3","article-title":"Gaussian processes and martingales for fuzzy-valued variables with continuous parameter","volume":"133","author":"Li","year":"2001","journal-title":"Inform. Sci."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB19","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0165-0114(93)90258-J","article-title":"On embedding problems of fuzzy number space","volume":"55","author":"Ma","year":"1993","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB20","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0165-0114(00)00092-0","article-title":"Separability for graph convergence of sequences of fuzzy-valued random variables","volume":"123","author":"Ogura","year":"2001","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S0218488501000570","article-title":"Set defuzzification and Choquet integral","volume":"9","author":"Ogura","year":"2001","journal-title":"J. Uncertainty, Fuzziness and Knowledge-Based Systems"},{"key":"10.1016\/S0165-0114(02)00145-8_BIB22","unstructured":"Y. Ogura, S. Li, A strong law of large numbers for fuzzy-valued random variables in the extended Hausdorff metric H\u221e, preprint."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB23","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0047-259X(85)90078-8","article-title":"On the theory of Banach space valued multifunctions, 1, Integration and conditional expectation","volume":"17","author":"Papageorgiou","year":"1985","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB24","unstructured":"F.N. Proske, M.L. Puri, Limit theorems for fuzzy random variables, to appear."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB25","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/0022-247X(86)90093-4","article-title":"Fuzzy random variables","volume":"114","author":"Puri","year":"1986","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB26","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0022-247X(91)90293-9","article-title":"Convergence theorem for fuzzy martingales","volume":"160","author":"Puri","year":"1991","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0165-0114(02)00145-8_BIB27","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1090\/S0002-9939-1952-0045938-2","article-title":"An embedding theorem for spaces of convex sets","volume":"3","author":"R\u0227dstr\u00f6m","year":"1952","journal-title":"Proc. Amer. Math. Soc."}],"container-title":["Fuzzy Sets and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011402001458?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011402001458?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T23:37:21Z","timestamp":1759016241000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165011402001458"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,5]]}},"alternative-id":["S0165011402001458"],"URL":"https:\/\/doi.org\/10.1016\/s0165-0114(02)00145-8","relation":{},"ISSN":["0165-0114"],"issn-type":[{"value":"0165-0114","type":"print"}],"subject":[],"published":{"date-parts":[[2003,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A convergence theorem of fuzzy-valued martingales in the extended Hausdorff metric","name":"articletitle","label":"Article Title"},{"value":"Fuzzy Sets and Systems","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0165-0114(02)00145-8","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2002 Elsevier Science B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}