{"id":"https://openalex.org/W1980851047","doi":"https://doi.org/10.1080/15501320802540710","title":"On the Approximation of Fuzzy System","display_name":"On the Approximation of Fuzzy System","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1980851047","doi":"https://doi.org/10.1080/15501320802540710","mag":"1980851047"},"language":"en","primary_location":{"id":"doi:10.1080/15501320802540710","is_oa":false,"landing_page_url":"https://doi.org/10.1080/15501320802540710","pdf_url":null,"source":{"id":"https://openalex.org/S64417657","display_name":"International Journal of Distributed Sensor Networks","issn_l":"1550-1329","issn":["1550-1329","1550-1477"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Distributed Sensor Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/dffab60eaa0f4d21b9228674931be259","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018962276","display_name":"Shihong Yue","orcid":"https://orcid.org/0000-0003-3473-2704"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shihong Yue","raw_affiliation_strings":["Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100344528","display_name":"Wei Chen","orcid":"https://orcid.org/0000-0003-0303-3978"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Chen","raw_affiliation_strings":["Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092021633","display_name":"Jin Wang","orcid":"https://orcid.org/0000-0002-6583-129X"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Wang","raw_affiliation_strings":["Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101809949","display_name":"Huaxiang Wang","orcid":"https://orcid.org/0000-0002-8792-0760"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huaxiang Wang","raw_affiliation_strings":["Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Senior Member, IEEE, School of Automation, Tianjin University, Tianjin, China#TAB#","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018962276"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":{"value":2200,"currency":"USD","value_usd":2200},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07818854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"1","first_page":"52","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9857000112533569,"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":0.9857000112533569,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9406999945640564,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6316925883293152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.531911313533783},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.5289331078529358},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5049331784248352},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.4894393980503082},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.48757070302963257},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.46927180886268616},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46387919783592224},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4635341167449951},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4633828401565552},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.42752954363822937},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.42422306537628174},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4190859794616699},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38749679923057556},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22925570607185364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19661131501197815}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6316925883293152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.531911313533783},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.5289331078529358},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5049331784248352},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.4894393980503082},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.48757070302963257},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.46927180886268616},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46387919783592224},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4635341167449951},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4633828401565552},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.42752954363822937},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.42422306537628174},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4190859794616699},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38749679923057556},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22925570607185364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19661131501197815}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/15501320802540710","is_oa":false,"landing_page_url":"https://doi.org/10.1080/15501320802540710","pdf_url":null,"source":{"id":"https://openalex.org/S64417657","display_name":"International Journal of Distributed Sensor Networks","issn_l":"1550-1329","issn":["1550-1329","1550-1477"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Distributed Sensor Networks","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:sae:intdis:v:5:y:2009:i:1:p:52-52","is_oa":false,"landing_page_url":"https://journals.sagepub.com/doi/10.1080/15501320802540710","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:dffab60eaa0f4d21b9228674931be259","is_oa":true,"landing_page_url":"https://doaj.org/article/dffab60eaa0f4d21b9228674931be259","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Distributed Sensor Networks, Vol 5, Iss 1, Pp 52-52 (2009)","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:dffab60eaa0f4d21b9228674931be259","is_oa":true,"landing_page_url":"https://doaj.org/article/dffab60eaa0f4d21b9228674931be259","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Distributed Sensor Networks, Vol 5, Iss 1, Pp 52-52 (2009)","raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","score":0.4099999964237213,"display_name":"No poverty"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1487720066","https://openalex.org/W2781808531","https://openalex.org/W4361984403","https://openalex.org/W1975005191","https://openalex.org/W2674573885","https://openalex.org/W2253053392","https://openalex.org/W2145270521","https://openalex.org/W2791187250","https://openalex.org/W3186561448","https://openalex.org/W2025902904"],"abstract_inverted_index":{"The":[0,74,271,278],"choice":[1,116],"of":[2,30,40,70,137,255,269,334,378],"fuzzy":[3,10,21,32,42,76,86,103,152,184,230,258,317,356,382],"set":[4,46,108,127,149,161],"function":[5,47,109,128,218,225,236],"affects":[6],"how":[7],"well":[8,165],"the":[9,28,31,35,63,68,101,114,122,124,131,135,142,201,215,228,256,266,315,332,340,354,374],"systems":[11,43,153,357],"approximate":[12,233],"an":[13,118,250,307,324],"unknown":[14],"function.":[15],"We":[16,98,178,211],"first":[17],"examine":[18],"several":[19],"popular":[20],"systems,":[22],"based":[23],"on":[24],"which":[25],"we":[26,245,261],"generalize":[27],"error":[29],"system":[33,77,87,104,185,231,318,326],"by":[34,111,265,362],"mathematical":[36,72,138],"functional.":[37,139],"Two":[38,368],"classes":[39],"extended":[41,75,183,229,257,316,355,381],"with":[44,105,197,237],"special":[45],"are":[48,60,95,291,370],"proposed":[49,182,380],"respectively":[50],"in":[51,61,67,134,222],"one-dimensional":[52],"and":[53,58,299,327,347,350,376],"two-dimensional":[54],"reproducing":[55,125,202,216],"kernel":[56,203,217],"spaces,":[57],"they":[59],"fact":[62],"best":[64,115,132],"interpolation":[65],"operators":[66],"sense":[69,136],"classical":[71],"approximation.":[73],"can":[78,129,163,232,328,358],"be":[79,359],"used":[80,283,371],"as":[81,83,96,297],"easily":[82,220],"any":[84,223,234],"typical":[85],"but":[88,166],"has":[89],"better":[90],"characters.":[91],"Our":[92],"major":[93],"contributions":[94],"follows.":[97],"prove":[99],"that":[100,214],"existing":[102],"a":[106,189,320],"triangle-shaped":[107],"is":[110,170,186,195,219,282,305],"no":[112],"means":[113],"for":[117,188],"uncertain":[119,191,325],"system.":[120,192,259],"On":[121],"contrary,":[123],"kernel-shaped":[126],"give":[130],"approximation":[133,252,280,309,322],"According":[140],"to":[141,154,173,207,284,323,372],"result,":[143],"overlapped":[144],"symmetric":[145],"triangles":[146],"or":[147,336,365],"trapezoid":[148],"functions":[150,162],"reduce":[151],"piecewise":[155],"linear":[156],"systems.":[157,383],"Universal":[158],"Gaussian":[159],"bell-curve":[160],"work":[164,329],"its":[167,209],"learning":[168],"cost":[169],"too":[171,205],"expensive":[172],"apply":[174],"under":[175,293,331],"online":[176],"condition.":[177],"explain":[179],"what":[180],"our":[181,379],"useful":[187],"given":[190],"This":[193],"solution":[194],"associated":[196],"another":[198],"problem:":[199],"Is":[200],"condition":[204,333],"specific":[206],"limit":[208],"applications?":[210],"must":[212],"stress":[213],"found":[221],"continuous":[224,235],"space.":[226],"Consequently,":[227,339],"arbitrary":[238],"accuracy.":[239],"Furthermore":[240],"one":[241],"may":[242],"question":[243],"why":[244],"do":[246,312],"not":[247],"directly":[248],"use":[249],"optimal":[251,279,308,345],"functional":[253,281,310],"instead":[254],"Here":[260],"answer":[262],"this":[263],"problem":[264],"following":[267],"point":[268],"views:":[270],"two":[272,341],"methods":[273,342],"face":[274],"different":[275,344,348],"applicable":[276],"conditions.":[277],"interpolate":[285],"those":[286],"accurate":[287],"data.":[288],"These":[289],"data":[290],"needed":[292],"certain":[294],"conditions":[295],"such":[296],"distributions":[298],"quantity,":[300],"etc.":[301],"When":[302],"little":[303],"information":[304],"available,":[306],"will":[311],"nothing.":[313],"But":[314],"gives":[319],"good":[321],"efficiently":[330],"vague":[335],"poor":[337],"information.":[338],"have":[343],"criteria":[346],"input":[349],"output":[351],"descriptions.":[352],"Furthermore,":[353],"created":[360],"flexibly":[361],"artificial":[363],"experiences":[364],"other":[366],"ways.":[367],"experiments":[369],"verify":[373],"effectiveness":[375],"efficiency":[377]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}