{"id":"https://openalex.org/W2091881098","doi":"https://doi.org/10.1016/s0165-0114(03)00142-8","title":"On the compactness of fuzzy numbers with sendograph metric","display_name":"On the compactness of fuzzy numbers with sendograph metric","publication_year":2003,"publication_date":"2003-04-30","ids":{"openalex":"https://openalex.org/W2091881098","doi":"https://doi.org/10.1016/s0165-0114(03)00142-8","mag":"2091881098"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-0114(03)00142-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(03)00142-8","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/A5009997455","display_name":"Taihe Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Taihe Fan","raw_affiliation_strings":["Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, China","Department of Mathematics; Ningbo University; Ningbo, Zhejiang 315211 China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, China","institution_ids":["https://openalex.org/I109935558"]},{"raw_affiliation_string":"Department of Mathematics; Ningbo University; Ningbo, Zhejiang 315211 China","institution_ids":["https://openalex.org/I109935558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009997455"],"corresponding_institution_ids":["https://openalex.org/I109935558"],"apc_list":{"value":2600,"currency":"USD","value_usd":2600},"apc_paid":null,"fwci":0.9892,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.79209262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"143","issue":"3","first_page":"471","last_page":"477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8852882385253906},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.7098883986473083},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6446094512939453},{"id":"https://openalex.org/keywords/product-metric","display_name":"Product metric","score":0.5996456146240234},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5964682698249817},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.566527247428894},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5284664034843445},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5283311605453491},{"id":"https://openalex.org/keywords/uniform-continuity","display_name":"Uniform continuity","score":0.5232345461845398},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.5122095942497253},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4926303029060364},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.48354053497314453},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4291929304599762},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.4216553270816803},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4170185327529907},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3831491470336914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20513847470283508},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07702445983886719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07199972867965698}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8852882385253906},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.7098883986473083},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6446094512939453},{"id":"https://openalex.org/C154497576","wikidata":"https://www.wikidata.org/wiki/Q7247777","display_name":"Product metric","level":3,"score":0.5996456146240234},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5964682698249817},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.566527247428894},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5284664034843445},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5283311605453491},{"id":"https://openalex.org/C129301229","wikidata":"https://www.wikidata.org/wiki/Q741865","display_name":"Uniform continuity","level":3,"score":0.5232345461845398},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.5122095942497253},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4926303029060364},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.48354053497314453},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4291929304599762},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4216553270816803},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4170185327529907},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3831491470336914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20513847470283508},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07702445983886719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07199972867965698},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0165-0114(03)00142-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0165-0114(03)00142-8","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1996865424","https://openalex.org/W2006127887","https://openalex.org/W2031747398","https://openalex.org/W2073945649","https://openalex.org/W2093827652","https://openalex.org/W2119645002","https://openalex.org/W2149271530"],"related_works":["https://openalex.org/W2563030166","https://openalex.org/W1996610422","https://openalex.org/W2354834258","https://openalex.org/W4297833754","https://openalex.org/W2291453617","https://openalex.org/W1569454118","https://openalex.org/W3103264541","https://openalex.org/W3117679268","https://openalex.org/W2082940521","https://openalex.org/W2985615289"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
