{"id":"https://openalex.org/W1983997485","doi":"https://doi.org/10.1016/s0165-0114(98)00188-2","title":"The law of large numbers for fuzzy numbers with unbounded supports","display_name":"The law of large numbers for fuzzy numbers with unbounded supports","publication_year":2000,"publication_date":"2000-12-01","ids":{"openalex":"https://openalex.org/W1983997485","doi":"https://doi.org/10.1016/s0165-0114(98)00188-2","mag":"1983997485"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-0114(98)00188-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(98)00188-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062572464","display_name":"Dug Hun Hong","orcid":"https://orcid.org/0000-0001-8268-3551"},"institutions":[{"id":"https://openalex.org/I39705031","display_name":"Catholic University of Daegu","ror":"https://ror.org/04fxknd68","country_code":"KR","type":"education","lineage":["https://openalex.org/I39705031"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Dug Hun Hong","raw_affiliation_strings":["School of Mechanical and Automotive Engineering, Catholic University of Taegu-Hyosung, Kyungbuk 712-703, South Korea"],"affiliations":[{"raw_affiliation_string":"School of Mechanical and Automotive Engineering, Catholic University of Taegu-Hyosung, Kyungbuk 712-703, South Korea","institution_ids":["https://openalex.org/I39705031"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075289985","display_name":"Paul I. Ro","orcid":"https://orcid.org/0000-0003-3515-706X"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul I. Ro","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA","Department of Mechanical and Aerospace Engineering , North Carolina State University , Raleigh, NC 27695, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering , North Carolina State University , Raleigh, NC 27695, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062572464"],"corresponding_institution_ids":["https://openalex.org/I39705031"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":1.6964,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.83949906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"116","issue":"2","first_page":"269","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9713000059127808,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9684000015258789,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.866937518119812},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.6384201645851135},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5613319873809814},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5129096508026123},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5073949694633484},{"id":"https://openalex.org/keywords/semi-infinite","display_name":"Semi-infinite","score":0.4585244059562683},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4123808741569519},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.32879185676574707},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3048807978630066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11195391416549683},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08624392747879028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08481734991073608}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.866937518119812},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.6384201645851135},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5613319873809814},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5129096508026123},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5073949694633484},{"id":"https://openalex.org/C194571181","wikidata":"https://www.wikidata.org/wiki/Q7449306","display_name":"Semi-infinite","level":2,"score":0.4585244059562683},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4123808741569519},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.32879185676574707},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3048807978630066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11195391416549683},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08624392747879028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08481734991073608},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0165-0114(98)00188-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(98)00188-2","pdf_url":null,"source":{"id":"https://openalex.org/S169411308","display_name":"Fuzzy Sets and Systems","issn_l":"0165-0114","issn":["0165-0114","1872-6801"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Sets and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1965083204","https://openalex.org/W1979756370","https://openalex.org/W2003147638","https://openalex.org/W2019950953","https://openalex.org/W2039568955","https://openalex.org/W2057938334","https://openalex.org/W2068855444","https://openalex.org/W2088734284","https://openalex.org/W2095039467","https://openalex.org/W2095054050","https://openalex.org/W2955198501","https://openalex.org/W4230588984","https://openalex.org/W4253152609","https://openalex.org/W4312837445"],"related_works":["https://openalex.org/W1607077238","https://openalex.org/W2955955822","https://openalex.org/W2396726025","https://openalex.org/W1486684451","https://openalex.org/W2116249946","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W4317826560"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
