{"id":"https://openalex.org/W2100991479","doi":"https://doi.org/10.1109/cdc.2008.4738897","title":"On the existence and uniqueness of solutions for the concept values in Fuzzy Cognitive Maps","display_name":"On the existence and uniqueness of solutions for the concept values in Fuzzy Cognitive Maps","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2100991479","doi":"https://doi.org/10.1109/cdc.2008.4738897","mag":"2100991479"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738897","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","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/A5011949101","display_name":"Yiannis S. Boutalis","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["DE","GR"],"is_corresponding":true,"raw_author_name":"Yiannis Boutalis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece","Department of Electrical, Electronic and Communication Engineering Chair of Automatic Control, University of Erlangen Nuremberg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece","institution_ids":["https://openalex.org/I147962203"]},{"raw_affiliation_string":"Department of Electrical, Electronic and Communication Engineering Chair of Automatic Control, University of Erlangen Nuremberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103535177","display_name":"Theodoros Kottas","orcid":null},"institutions":[{"id":"https://openalex.org/I147962203","display_name":"Democritus University of Thrace","ror":"https://ror.org/03bfqnx40","country_code":"GR","type":"education","lineage":["https://openalex.org/I147962203"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Theodoros Kottas","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Democritus University of Thrace, Thrace, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Democritus University of Thrace, Thrace, Greece","institution_ids":["https://openalex.org/I147962203"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109251859","display_name":"Manolis A. Christodoulou","orcid":null},"institutions":[{"id":"https://openalex.org/I55741626","display_name":"Technical University of Crete","ror":"https://ror.org/03f8bz564","country_code":"GR","type":"education","lineage":["https://openalex.org/I55741626"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Manolis Christodoulou","raw_affiliation_strings":["Electronic and Computer Engineering, Technical University of Crete, Crete, Greece"],"affiliations":[{"raw_affiliation_string":"Electronic and Computer Engineering, Technical University of Crete, Crete, Greece","institution_ids":["https://openalex.org/I55741626"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011949101"],"corresponding_institution_ids":["https://openalex.org/I147962203","https://openalex.org/I181369854"],"apc_list":null,"apc_paid":null,"fwci":4.5764,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94469741,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"98","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12805","display_name":"Cognitive Science and Mapping","score":1.0,"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/T12805","display_name":"Cognitive Science and Mapping","score":1.0,"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/T14512","display_name":"Technology and Human Factors in Education and Health","score":0.914900004863739,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.9018996953964233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6085924506187439},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.5546798706054688},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5060877203941345},{"id":"https://openalex.org/keywords/fuzzy-cognitive-map","display_name":"Fuzzy cognitive map","score":0.49647384881973267},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.47892579436302185},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4729064702987671},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.4446038603782654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4376141428947449},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.4229733347892761},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.35465723276138306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3490387797355652},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.28371939063072205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19621950387954712},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1760038137435913}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.9018996953964233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6085924506187439},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.5546798706054688},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5060877203941345},{"id":"https://openalex.org/C5041914","wikidata":"https://www.wikidata.org/wiki/Q5511107","display_name":"Fuzzy cognitive map","level":5,"score":0.49647384881973267},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.47892579436302185},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4729064702987671},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.4446038603782654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4376141428947449},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.4229733347892761},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.35465723276138306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3490387797355652},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.28371939063072205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19621950387954712},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1760038137435913},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2008.4738897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738897","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W202391078","https://openalex.org/W1489140035","https://openalex.org/W1510377302","https://openalex.org/W1524987130","https://openalex.org/W1598733259","https://openalex.org/W1889110788","https://openalex.org/W1902052229","https://openalex.org/W1966153007","https://openalex.org/W1977575836","https://openalex.org/W2020948452","https://openalex.org/W2066031679","https://openalex.org/W2072934801","https://openalex.org/W2088903882","https://openalex.org/W2089103439","https://openalex.org/W2090009166","https://openalex.org/W2095224843","https://openalex.org/W2097415784","https://openalex.org/W2098378004","https://openalex.org/W2098561270","https://openalex.org/W2114197357","https://openalex.org/W2114956682","https://openalex.org/W2137521045","https://openalex.org/W2158284104","https://openalex.org/W2162338797","https://openalex.org/W2176864480","https://openalex.org/W2536526822","https://openalex.org/W6608307189","https://openalex.org/W6631298006","https://openalex.org/W6733400503"],"related_works":["https://openalex.org/W2070616933","https://openalex.org/W4362513838","https://openalex.org/W2354519566","https://openalex.org/W2899135524","https://openalex.org/W2747524643","https://openalex.org/W2115499189","https://openalex.org/W2809143454","https://openalex.org/W2373586056","https://openalex.org/W2388966578","https://openalex.org/W2620347228"],"abstract_inverted_index":{"Fuzzy":[0],"cognitive":[1,155],"maps":[2],"(FCM)":[3],"have":[4],"been":[5,23],"introduced":[6],"by":[7,67],"Kosko":[8],"to":[9,46,91],"model":[10],"complex":[11],"behavioral":[12],"systems":[13],"in":[14],"various":[15],"scientific":[16],"areas.":[17],"One":[18],"issue":[19],"that":[20,78],"has":[21],"not":[22,114],"adequately":[24],"studied":[25],"so":[26],"far":[27],"is":[28,44,76],"the":[29,48,63,80,86,96,100,106,109,125,128,139,153],"conditions":[30,85],"under":[31],"which":[32],"they":[33],"reach":[34],"a":[35,92],"certain":[36,84],"equilibrium":[37,112],"point":[38],"after":[39],"an":[40,69],"initial":[41,101],"perturbation.":[42],"This":[43],"equivalent":[45],"studying":[47],"existence":[49,64,107],"and":[50,134],"uniqueness":[51,110],"of":[52,65,99,111,130,141,145,151],"solutions":[53,66],"for":[54,127],"their":[55],"concept":[56,87,102,140],"values.":[57],"In":[58,143],"this":[59],"paper,":[60],"we":[61],"study":[62],"using":[68],"appropriately":[70],"defined":[71],"contraction":[72],"mapping":[73],"theorem.":[74],"It":[75],"proved":[77],"when":[79],"weight":[81],"interconnections":[82],"fulfill":[83],"values":[88,98,103],"will":[89],"converge":[90],"unique":[93],"solution":[94],"regardless":[95],"exact":[97],"perturbations.":[104],"Otherwise":[105],"or":[108],"can":[113],"be":[115],"assured.":[116],"The":[117],"results":[118,147],"are":[119,157],"considered":[120],"very":[121],"significant":[122],"because":[123],"set":[124],"basis":[126],"development":[129],"reliable":[131],"system":[132],"identification":[133],"control":[135],"schemes":[136],"based":[137],"on":[138],"FCM.":[142],"view":[144],"these":[146],"recently":[148],"proposed":[149],"extensions":[150],"FCM,":[152],"fuzzy":[154],"networks":[156],"invoked.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2014,"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"}
