{"id":"https://openalex.org/W2152892562","doi":"https://doi.org/10.1109/tfuzz.2008.2005010","title":"Fuzzy Solutions to Partial Differential Equations: Adaptive Approach","display_name":"Fuzzy Solutions to Partial Differential Equations: Adaptive Approach","publication_year":2008,"publication_date":"2008-08-28","ids":{"openalex":"https://openalex.org/W2152892562","doi":"https://doi.org/10.1109/tfuzz.2008.2005010","mag":"2152892562"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2008.2005010","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2008.2005010","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy 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/A5065136919","display_name":"Yung\u2010Yue Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yung-Yue Chen","raw_affiliation_strings":["Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110703362","display_name":"Yu-Te Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Te Chang","raw_affiliation_strings":["Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038219293","display_name":"Bor\u2010Sen Chen","orcid":"https://orcid.org/0000-0003-1644-6106"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Bor-Sen Chen","raw_affiliation_strings":["Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Control and Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1143,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.94000236,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"116","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9876999855041504,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9599999785423279,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/mathematics","display_name":"Mathematics","score":0.718456506729126},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6463389992713928},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6265078783035278},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4865335524082184},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4341869354248047},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4209447503089905},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.39947253465652466},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3864717185497284},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22944313287734985},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1970079243183136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07474362850189209}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.718456506729126},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6463389992713928},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6265078783035278},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4865335524082184},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4341869354248047},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4209447503089905},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.39947253465652466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3864717185497284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22944313287734985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1970079243183136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07474362850189209},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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:10.1109/tfuzz.2008.2005010","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2008.2005010","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8700000047683716,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W130083205","https://openalex.org/W143857792","https://openalex.org/W562026345","https://openalex.org/W573209145","https://openalex.org/W637288233","https://openalex.org/W1481731550","https://openalex.org/W1487127700","https://openalex.org/W1968559856","https://openalex.org/W1988896985","https://openalex.org/W2022910713","https://openalex.org/W2029682651","https://openalex.org/W2038055297","https://openalex.org/W2047993072","https://openalex.org/W2068052921","https://openalex.org/W2073220658","https://openalex.org/W2075194837","https://openalex.org/W2075594316","https://openalex.org/W2077658674","https://openalex.org/W2079325629","https://openalex.org/W2103414828","https://openalex.org/W2105072582","https://openalex.org/W2109911863","https://openalex.org/W2114020393","https://openalex.org/W2126611084","https://openalex.org/W2131465376","https://openalex.org/W2136504686","https://openalex.org/W2142581072","https://openalex.org/W2146096764","https://openalex.org/W2162232298","https://openalex.org/W2798735774","https://openalex.org/W4212997115","https://openalex.org/W4213345774","https://openalex.org/W4233865791","https://openalex.org/W4302572442"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2281834912","https://openalex.org/W2541537839","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":{"A":[0],"new":[1],"technique":[2],"using":[3],"an":[4,79,85],"adaptive":[5,42,64],"fuzzy":[6,29,45,49,97,105],"algorithm":[7],"to":[8,12,26,31,40,101],"obtain":[9],"the":[10,34,41,55,68,72,91,95,102,115,127,136,156],"solutions":[11,153],"a":[13,28,48,61,141],"class":[14],"of":[15,44,63,104,117,143],"partial":[16],"differential":[17],"equations":[18,119],"(PDEs)":[19],"is":[20,25,57,75,123],"presented.":[21],"The":[22],"design":[23],"objective":[24],"find":[27],"solution":[30,50,93,98,108],"satisfy":[32],"precisely":[33],"PDEs":[35,144],"with":[36,51,99,152],"boundary":[37],"conditions.":[38],"According":[39],"scheme":[43],"logic":[46],"systems,":[47],"adjustable":[52],"parameters":[53,70],"for":[54,66],"PDE":[56],"first":[58],"described.":[59],"Then,":[60],"set":[62],"laws":[65],"tuning":[67],"free":[69],"in":[71,120,146],"consequent":[73],"part":[74],"derived":[76],"from":[77,126],"minimizing":[78],"appropriate":[80],"error":[81,88,118],"function.":[82],"In":[83,130],"addition,":[84],"elegant":[86],"approximated":[87],"bound":[89],"between":[90],"exact":[92],"and":[94,107],"proposed":[96,137],"respect":[100],"number":[103],"rules":[106],"errors":[109],"has":[110],"also":[111,124,150],"been":[112],"derived.":[113],"Furthermore,":[114],"convergence":[116],"mesh":[121],"points":[122],"discussed":[125],"energy":[128],"perspective.":[129],"this":[131],"paper,":[132],"we":[133],"show":[134],"that":[135],"method":[138],"can":[139],"solve":[140],"variety":[142],"encountered":[145],"engineering.":[147],"Comparisons":[148],"are":[149],"made":[151],"obtained":[154],"by":[155],"finite-element":[157],"method.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
