{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1361699994246558592.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1098/rspa.1986.0091"}},{"identifier":{"@type":"URI","@value":"https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1986.0091"}},{"identifier":{"@type":"URI","@value":"https://royalsocietypublishing.org/rspa/article-pdf/407/1832/171/66300/rspa.1986.0091.pdf"}},{"identifier":{"@type":"NAID","@value":"30035350792"}}],"dc:title":[{"@value":"Limit theorems for fuzzy random variables"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>Abstract</jats:title>\n                  <jats:p>A strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables, whose values are fuzzy sets with compact levels. The proofs are based on embedding theorems as well as on probability techniques in Banach space.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380306912562575362","@type":"Researcher","foaf:name":[{"@value":"E. P. Klement"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221, U. S. A."}]},{"@id":"https://cir.nii.ac.jp/crid/1380306912562575361","@type":"Researcher","foaf:name":[{"@value":"M. L. Puri"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U. S. A."}]},{"@id":"https://cir.nii.ac.jp/crid/1380306912562575360","@type":"Researcher","foaf:name":[{"@value":"D. A. Ralescu"}],"jpcoar:affiliationName":[{"@value":"Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221, U. S. A"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00804630"},{"@type":"EISSN","@value":"20539169"}],"prism:publicationName":[{"@value":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences"}],"dc:publisher":[{"@value":"The Royal Society"}],"prism:publicationDate":"1986-09-08","prism:volume":"407","prism:number":"1832","prism:startingPage":"171","prism:endingPage":"182"},"reviewed":"false","dc:rights":["https://royalsociety.org/journals/ethics-policies/data-sharing-mining/"],"url":[{"@id":"https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1986.0091"},{"@id":"https://royalsocietypublishing.org/rspa/article-pdf/407/1832/171/66300/rspa.1986.0091.pdf"}],"createdAt":"2006-12-18","modifiedAt":"2026-02-25","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1390001204339756928","@type":"Article","relationType":["isReferencedBy","isCitedBy"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"ある種のファジィ確率ベクトルについての一考察"},{"@language":"en","@value":"On a Class of Fuzzy Random Vectors"},{"@language":"ja-Kana","@value":"アルシュ ノ ファジィ カクリツ ベクトル ニ ツイテ ノ イチコウサツ"}]},{"@id":"https://cir.nii.ac.jp/crid/1390001288034803328","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"On Law of Large Numbers for a Class of Fuzzy Random Vectors"}]},{"@id":"https://cir.nii.ac.jp/crid/1390282679316816000","@type":"Article","relationType":["isReferencedBy","isCitedBy"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"ランダム集合と大数の法則(<特集>確率ファジィ解析とその周辺)"},{"@language":"en","@value":"Random Sets and Laws of Large Numbers"},{"@value":"ランダム集合と大数の法則"},{"@language":"ja-Kana","@value":"ランダム シュウゴウ ト タイスウ ノ ホウソク"}]},{"@id":"https://cir.nii.ac.jp/crid/1390282763010438144","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"On the Set Representation of Fuzzy Random Vectors Obtained as Vague Perception of Random Phenomena"}]},{"@id":"https://cir.nii.ac.jp/crid/1390286981363421312","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"SET-VALUED AND FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS IN M-TYPE 2 BANACH SPACES"}]},{"@id":"https://cir.nii.ac.jp/crid/1390564237988216320","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Multi-Dimensional Fuzzy Random Variables"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1098/rspa.1986.0091"},{"@type":"CIA","@value":"30035350792"},{"@type":"CROSSREF","@value":"10.5687/sss.1994.169_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"},{"@type":"CROSSREF","@value":"10.5687/sss.1998.45_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"},{"@type":"CROSSREF","@value":"10.2748/tmj/1446818557_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"},{"@type":"CROSSREF","@value":"10.5687/sss.1996.77_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"},{"@type":"CROSSREF","@value":"10.3156/jfuzzy.10.6_1035_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"},{"@type":"CROSSREF","@value":"10.3156/jfuzzy.10.3_499_references_DOI_60eoOghalkqLGBhe291h9DUxk4Z"}]}