{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T06:11:32Z","timestamp":1778998292366,"version":"3.51.4"},"reference-count":42,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61403360"],"award-info":[{"award-number":["61403360"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374082"],"award-info":[{"award-number":["61374082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Fuzzy Syst."],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1109\/tfuzz.2015.2466080","type":"journal-article","created":{"date-parts":[[2015,8,13]],"date-time":"2015-08-13T16:16:02Z","timestamp":1439482562000},"page":"615-621","source":"Crossref","is-referenced-by-count":79,"title":["Law of Large Numbers for Uncertain Random Variables"],"prefix":"10.1109","volume":"24","author":[{"given":"Kai","family":"Yao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinwu","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1002\/int.21681"},{"key":"ref38","article-title":"Uncertain random logic and uncertain random entailment","author":"liu","year":"2012"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-014-0985-5"},{"key":"ref32","article-title":"Uncertain random goal programming","author":"qin","year":"2013"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-014-9183-3"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9149-2"},{"key":"ref37","first-page":"3","article-title":"Uncertain random graph and uncertain random network","volume":"8","author":"liu","year":"2014","journal-title":"J Uncertain Syst"},{"key":"ref36","article-title":"Reliability analysis in uncertain random system","author":"wen","year":"2012"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1142\/S021848851450024X"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1361-2"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/978-3-540-27774-3_17","article-title":"Preservation of distinguished fuzzy measure classes by distortion","author":"val\u00e1\u0161kov\u00e1","year":"2004","journal-title":"Modeling Decisions for Artificial Intelligence"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2014.2360551"},{"key":"ref11","first-page":"205","article-title":"Classes of fuzzy measures and distortion","volume":"41","author":"val\u00e1\u0161kov\u00e1","year":"2005","journal-title":"Kybernetika"},{"key":"ref12","first-page":"643","article-title":"Construction of aggregation operators: New composition method","volume":"39","author":"calvo","year":"2003","journal-title":"Kybernetika"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-005-0525-5"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90147-V"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00048-8"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00188-2"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(78)90019-1"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(79)90020-3"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(82)90049-4"},{"key":"ref28","first-page":"232","article-title":"Maximum entropy principle for uncertain variables","volume":"13","author":"chen","year":"2011","journal-title":"Int J Fuzzy Syst"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01212011"},{"key":"ref27","first-page":"181","article-title":"Expected value of function of uncertain variables","volume":"4","author":"liu","year":"2010","journal-title":"J Uncertain Syst"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994517"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1214\/aop\/1079021467","article-title":"A law of large numbers for random walks in random mixing environments","volume":"32","author":"comets","year":"2004","journal-title":"Ann Probab"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0935-0"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(00)00116-4"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.09.002"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996029"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90029-5"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1965-0198524-1"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(84)90033-2"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00392-8"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90132-A"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1186\/2195-5468-2-14"},{"key":"ref24","author":"liu","year":"2007","journal-title":"Uncertainty Theory"},{"key":"ref41","author":"liu","year":"2010","journal-title":"Uncertainty Theory A Branch of Mathematics for Modeling Human Uncertainty"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(99)00140-2"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1080\/09720502.2010.10700701"},{"key":"ref25","first-page":"3","article-title":"Some research problems in uncertainty theory","volume":"3","author":"liu","year":"2009","journal-title":"J Uncertain Syst"}],"container-title":["IEEE Transactions on Fuzzy Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/91\/7480878\/07182284.pdf?arnumber=7182284","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T02:34:49Z","timestamp":1633919689000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7182284\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6]]},"references-count":42,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1109\/tfuzz.2015.2466080","relation":{},"ISSN":["1063-6706","1941-0034"],"issn-type":[{"value":"1063-6706","type":"print"},{"value":"1941-0034","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6]]}}}