{"id":"https://openalex.org/W2129708481","doi":"https://doi.org/10.1109/fuzzy.2005.1452522","title":"Separable Approximation Property of Hierarchical Fuzzy Systems","display_name":"Separable Approximation Property of Hierarchical Fuzzy Systems","publication_year":2005,"publication_date":"2005-07-27","ids":{"openalex":"https://openalex.org/W2129708481","doi":"https://doi.org/10.1109/fuzzy.2005.1452522","mag":"2129708481"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2005.1452522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2005.1452522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05.","raw_type":"proceedings-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/A5077623520","display_name":"Xiao\u2010Jun Zeng","orcid":"https://orcid.org/0000-0002-2320-2495"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Xiao-Jun Zeng","raw_affiliation_strings":["School of Informatics, University of Manchester, Institute of Science and Technology, Manchester, UK","Sch. of Informatics, Manchester Univ.#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Manchester, Institute of Science and Technology, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Informatics, Manchester Univ.#TAB#","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105350782","display_name":"John Keane","orcid":"https://orcid.org/0000-0001-9022-4339"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J.A. Keane","raw_affiliation_strings":["School of Informatics, University of Manchester, Institute of Science and Technology, Manchester, UK","Sch. of Informatics, Manchester Univ.#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Manchester, Institute of Science and Technology, Manchester, UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Sch. of Informatics, Manchester Univ.#TAB#","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077623520"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":0.8775,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8112019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":null,"first_page":"951","last_page":"956"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.9758999943733215,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/separable-space","display_name":"Separable space","score":0.7469425201416016},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6769065260887146},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.545341968536377},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.500636100769043},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4970381557941437},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.46290621161460876},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4588847756385803},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.43202102184295654},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42293378710746765},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.41637781262397766},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37289363145828247},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3373190760612488},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3367358446121216},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.228775292634964},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08509397506713867},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07236331701278687}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.7469425201416016},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6769065260887146},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.545341968536377},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.500636100769043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4970381557941437},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.46290621161460876},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4588847756385803},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.43202102184295654},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42293378710746765},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.41637781262397766},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37289363145828247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3373190760612488},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3367358446121216},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.228775292634964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08509397506713867},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07236331701278687},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2005.1452522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2005.1452522","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1892399156","https://openalex.org/W1996162276","https://openalex.org/W2001852281","https://openalex.org/W2002041997","https://openalex.org/W2020136781","https://openalex.org/W2026223306","https://openalex.org/W2027402490","https://openalex.org/W2065208924","https://openalex.org/W2089767545","https://openalex.org/W2098593580","https://openalex.org/W2102634648","https://openalex.org/W2103269436","https://openalex.org/W2104187566","https://openalex.org/W2107473902","https://openalex.org/W2124065547","https://openalex.org/W2128974325","https://openalex.org/W2133954889","https://openalex.org/W2140662276","https://openalex.org/W2152187914","https://openalex.org/W2153649435","https://openalex.org/W2155210646","https://openalex.org/W2156938625","https://openalex.org/W2162450741","https://openalex.org/W2168448725","https://openalex.org/W2740440199","https://openalex.org/W4232514889"],"related_works":["https://openalex.org/W2253053392","https://openalex.org/W2184441312","https://openalex.org/W2121560876","https://openalex.org/W4206081075","https://openalex.org/W2331106272","https://openalex.org/W2366385051","https://openalex.org/W1470403688","https://openalex.org/W1486684451","https://openalex.org/W4361984403","https://openalex.org/W4361273540"],"abstract_inverted_index":{"This":[0,55],"paper":[1],"discusses":[2],"the":[3,30,45,71,79],"capabilities":[4],"of":[5,22,32,48,83],"standard":[6],"hierarchical":[7,16,23,34,63,84],"fuzzy":[8,24,35,64,85],"systems":[9,25,65,86],"to":[10,61],"approximate":[11],"continuous":[12],"functions":[13],"with":[14,37,51],"natural":[15],"structure.":[17],"The":[18],"separable":[19,72],"approximation":[20,39,53,73,81],"property":[21,56,82],"is":[26,76],"proved,":[27],"that":[28],"is,":[29],"construction":[31,47],"a":[33,58],"system":[36],"required":[38,52],"accuracy":[40],"can":[41],"be":[42],"achieved":[43],"by":[44],"separate":[46],"each":[49],"sub-system":[50],"accuracy.":[54],"provides":[57],"simple":[59],"method":[60],"construct":[62],"for":[66],"function":[67],"approximation.":[68],"Based":[69],"on":[70],"property,":[74],"it":[75],"further":[77],"proved":[78],"structure":[80]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
