{"id":"https://openalex.org/W2124320708","doi":"https://doi.org/10.1109/tsmcb.2012.2217323","title":"Takagi\u2013Sugeno Fuzzy Models in the Framework of Orthonormal Basis Functions","display_name":"Takagi\u2013Sugeno Fuzzy Models in the Framework of Orthonormal Basis Functions","publication_year":2012,"publication_date":"2012-10-19","ids":{"openalex":"https://openalex.org/W2124320708","doi":"https://doi.org/10.1109/tsmcb.2012.2217323","mag":"2124320708","pmid":"https://pubmed.ncbi.nlm.nih.gov/23096073"},"language":"en","primary_location":{"id":"doi:10.1109/tsmcb.2012.2217323","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2012.2217323","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.1109/TSMCB.2012.2217323","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047947883","display_name":"Jeremias Barbosa Machado","orcid":"https://orcid.org/0009-0001-6986-8751"},"institutions":[{"id":"https://openalex.org/I107613613","display_name":"Information Technology Institute","ror":"https://ror.org/04ynw2g14","country_code":"EG","type":"facility","lineage":["https://openalex.org/I107613613"]},{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR","EG"],"is_corresponding":true,"raw_author_name":"J. B. Machado","raw_affiliation_strings":["Systems Engineering and Information Technology Institute, Federal University of Itajub\u00e1 (UNIFEI), CEP 37500-903 Itajub\u00e1, MG, Brazil. jeremias@unifei.edu.br","Syst. Eng. & Inf. Technol. Inst., Fed. Univ. of Itajuba (UNIFEI), Itajuba, Brazil"],"affiliations":[{"raw_affiliation_string":"Systems Engineering and Information Technology Institute, Federal University of Itajub\u00e1 (UNIFEI), CEP 37500-903 Itajub\u00e1, MG, Brazil. jeremias@unifei.edu.br","institution_ids":["https://openalex.org/I8165072"]},{"raw_affiliation_string":"Syst. Eng. & Inf. Technol. Inst., Fed. Univ. of Itajuba (UNIFEI), Itajuba, Brazil","institution_ids":["https://openalex.org/I107613613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109246631","display_name":"R. J. G. B. Campello","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"R. J. G. B. Campello","raw_affiliation_strings":["Department of Computer Sciences, University of S\u00e3o Paulo, Sao Carlos, Sao Paulo, Brazil","[Department of Computer Science, University of S\u00e3o Paulo, Sao Carlos, Brazil]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, University of S\u00e3o Paulo, Sao Carlos, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]},{"raw_affiliation_string":"[Department of Computer Science, University of S\u00e3o Paulo, Sao Carlos, Brazil]","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112428259","display_name":"W.C. Amaral","orcid":null},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"W. C. Amaral","raw_affiliation_strings":["Department of Computer Engineering and Industrial Automation, State University of Campinas, Campinas, Sao Paulo, Brazil","Dept. of Comput. Eng. & Ind. Autom., State Univ. of Campinas (UNICAMP), Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Industrial Automation, State University of Campinas, Campinas, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"Dept. of Comput. Eng. & Ind. Autom., State Univ. of Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047947883"],"corresponding_institution_ids":["https://openalex.org/I107613613","https://openalex.org/I8165072"],"apc_list":null,"apc_paid":null,"fwci":1.7685,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.87183315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"43","issue":"3","first_page":"858","last_page":"870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10320","display_name":"Neural Networks and Applications","score":0.9958000183105469,"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":0.9854000210762024,"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/orthonormal-basis","display_name":"Orthonormal basis","score":0.8099486231803894},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.654719889163971},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6341641545295715},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5903502702713013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5884619355201721},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5647193193435669},{"id":"https://openalex.org/keywords/fuzzy-rule","display_name":"Fuzzy rule","score":0.5082935690879822},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49074065685272217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4449394643306732},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.4121939241886139},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.38794323801994324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33217987418174744},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15685942769050598},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0877651572227478}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8099486231803894},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.654719889163971},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6341641545295715},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5903502702713013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5884619355201721},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5647193193435669},{"id":"https://openalex.org/C2780049643","wikidata":"https://www.wikidata.org/wiki/Q5511139","display_name":"Fuzzy rule","level":4,"score":0.5082935690879822},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49074065685272217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4449394643306732},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.4121939241886139},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.38794323801994324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33217987418174744},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15685942769050598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0877651572227478},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017143","descriptor_name":"Fuzzy Logic","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":4,"locations":[{"id":"doi:10.1109/tsmcb.2012.2217323","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2012.2217323","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:23096073","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/23096073","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null},{"id":"pmh:002314191","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/TSMCB.2012.2217323","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:researchonline.jcu.edu.au:47673","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400519","display_name":"ResearchOnline at James Cook University (James Cook University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I86467917","host_organization_name":"James Cook University","host_organization_lineage":["https://openalex.org/I86467917"],"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"}],"best_oa_location":{"id":"pmh:002314191","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/TSMCB.2012.2217323","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W616910851","https://openalex.org/W1490488263","https://openalex.org/W1853840354","https://openalex.org/W1970730075","https://openalex.org/W1987801991","https://openalex.org/W1991777572","https://openalex.org/W2002041442","https://openalex.org/W2002041997","https://openalex.org/W2018592739","https://openalex.org/W2027500037","https://openalex.org/W2028702048","https://openalex.org/W2037950596","https://openalex.org/W2046162917","https://openalex.org/W2055337535","https://openalex.org/W2079325629","https://openalex.org/W2079543542","https://openalex.org/W2080138696","https://openalex.org/W2081103703","https://openalex.org/W2083879071","https://openalex.org/W2089767545","https://openalex.org/W2093846413","https://openalex.org/W2095753402","https://openalex.org/W2101036899","https://openalex.org/W2101566415","https://openalex.org/W2115844704","https://openalex.org/W2123186004","https://openalex.org/W2128526375","https://openalex.org/W2129649323","https://openalex.org/W2135646102","https://openalex.org/W2140834769","https://openalex.org/W2145479133","https://openalex.org/W2146109515","https://openalex.org/W2152421133","https://openalex.org/W2158290540","https://openalex.org/W2167259173","https://openalex.org/W2169654918","https://openalex.org/W2171975443","https://openalex.org/W2221304078","https://openalex.org/W3147239081","https://openalex.org/W4233391551","https://openalex.org/W4235848843"],"related_works":["https://openalex.org/W2149054915","https://openalex.org/W1547339931","https://openalex.org/W1496788307","https://openalex.org/W2015817211","https://openalex.org/W2044409786","https://openalex.org/W2383575531","https://openalex.org/W2729152297","https://openalex.org/W2386104798","https://openalex.org/W1976397437","https://openalex.org/W2108026032"],"abstract_inverted_index":{"An":[0,183],"approach":[1,26,193],"to":[2,86,151,154,180,187],"obtain":[3],"Takagi-Sugeno":[4],"(TS)":[5],"fuzzy":[6,44,94,110,130],"models":[7,36],"of":[8,15,50,84,96,104,145,191,197],"nonlinear":[9,139,200],"dynamic":[10,201],"systems":[11],"using":[12,137],"the":[13,43,48,51,59,90,97,121,152,167,178,189,195],"framework":[14],"orthonormal":[16,91],"basis":[17],"functions":[18,85],"(OBFs)":[19],"is":[20,27,66,185],"presented":[21,186],"in":[22,32,89,194],"this":[23,192],"paper.":[24],"This":[25],"based":[28,108],"on":[29,77,109,173],"an":[30,146],"architecture":[31],"which":[33,170],"local":[34],"linear":[35],"with":[37,149],"ladder-structured":[38],"generalized":[39],"OBFs":[40],"(GOBFs)":[41],"constitute":[42],"rule":[45,60],"consequents":[46],"and":[47,112,120,129],"outputs":[49],"corresponding":[52],"GOBF":[53,126],"filters":[54],"are":[55,99,117,133,157],"input":[56],"variables":[57],"for":[58,166],"antecedents.":[61],"The":[62,93,142],"resulting":[63],"GOBF-TS":[64],"model":[65,98,122],"characterized":[67],"by":[68,102,136],"having":[69],"only":[70],"real-valued":[71],"parameters":[72,123,153],"that":[73],"do":[74],"not":[75],"depend":[76],"any":[78],"user":[79],"specification":[80],"about":[81],"particular":[82],"types":[83],"be":[87,155,181],"used":[88],"basis.":[92],"rules":[95,116],"initially":[100],"obtained":[101],"means":[103],"a":[105,138,198],"well-known":[106],"technique":[107],"clustering":[111],"least":[113],"squares.":[114],"Those":[115,160],"then":[118],"simplified,":[119],"(GOBF":[124],"poles,":[125],"expansion":[127],"coefficients,":[128],"membership":[131],"functions)":[132],"subsequently":[134],"adjusted":[135],"optimization":[140,168],"algorithm.":[141],"exact":[143,163],"gradients":[144,161],"error":[147],"functional":[148],"respect":[150],"optimized":[156],"computed":[158],"analytically.":[159],"provide":[162],"search":[164],"directions":[165],"process,":[169],"relies":[171],"solely":[172],"input-output":[174],"data":[175],"measured":[176],"from":[177],"system":[179],"modeled.":[182],"example":[184],"illustrate":[188],"performance":[190],"modeling":[196],"complex":[199],"system.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}