{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T13:27:18Z","timestamp":1777382838970,"version":"3.51.4"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:p> In this paper, we shall present weak and strong laws of large numbers (WLLN's and SLLN's) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric [Formula: see text], based on the result of set-valued random variable obtained by Taylor and Inoue<jats:sup>32,33<\/jats:sup>. This work is a continuation of Li and Ogura<jats:sup>20<\/jats:sup>. <\/jats:p>","DOI":"10.1142\/s0218488504003223","type":"journal-article","created":{"date-parts":[[2005,3,16]],"date-time":"2005-03-16T12:00:57Z","timestamp":1110974457000},"page":"811-825","source":"Crossref","is-referenced-by-count":12,"title":["LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF FUZZY SET-VALUED RANDOM VARIABLES"],"prefix":"10.1142","volume":"12","author":[{"given":"LI","family":"GUAN","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics,  Beijing University of Technology, 100 Ping Le Yuan,  Chao Yang District, Beijing, 100022, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SHOUMEI","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics,  Beijing University of Technology, 100 Ping Le Yuan,  Chao Yang District, Beijing, 100022, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996275"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(65)90049-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s004400050229"},{"key":"rf4","volume-title":"Fuzzy Systems and Mathematics","author":"Chen Y.","year":"1984"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/1427005"},{"key":"rf6","unstructured":"G.\u00a0Debreu, Proc. Fifth Berkeley Symposium Math. Stat. and Probability II, eds. L.\u00a0Lecam, J.\u00a0Neyman and E. L.\u00a0Scott (Univ. Calif. Press, Berkeley, 1966)\u00a0pp. 351\u2013372."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064267"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90132-A"},{"key":"rf9","first-page":"519","volume":"288","author":"Hess C.","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(77)90037-9"},{"key":"rf12","volume-title":"Theory of Correspondences Including Applications to Mathematical Economics","author":"Klein E.","year":"1984"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1986.0091"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(82)90049-4"},{"key":"rf15","first-page":"905","volume":"4","author":"Li S.","journal-title":"J. Fuzzy Math."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00092-4"},{"key":"rf17","first-page":"1384","volume":"26","author":"Li S.","journal-title":"Ann. Probab."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1800-0_5"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00145-8"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9932-0"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(03)00397-4"},{"key":"rf23","volume-title":"Random Sets and Integral Geometry","author":"Matheron G.","year":"1975"},{"key":"rf24","first-page":"249","volume":"235","author":"Molchanov I. S.","journal-title":"J. Math. Anal. Appl."},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00092-0"},{"key":"rf26","first-page":"769","volume":"15","author":"Prutti W.","journal-title":"J. Math. Mech."},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993671"},{"key":"rf28","first-page":"406","volume":"114","author":"Puri M. L.","journal-title":"J. Math. Anal. Appl."},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100046685"},{"key":"rf30","series-title":"Lect. Notes Math.","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0063205","volume-title":"Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces","volume":"672","author":"Taylor R. L.","year":"1978"},{"key":"rf31","first-page":"403","volume":"13","author":"Taylor R. L.","journal-title":"Bull. Instit. Math. Academia Sinica"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1080\/07362998508809069"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"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\/S0218488504003223","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:00:11Z","timestamp":1565146811000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488504003223"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,12]]},"references-count":31,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2004,12]]}},"alternative-id":["10.1142\/S0218488504003223"],"URL":"https:\/\/doi.org\/10.1142\/s0218488504003223","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,12]]}}}