{"id":"https://openalex.org/W2165878760","doi":"https://doi.org/10.1109/tpami.1985.4767725","title":"Incorporating Fuzzy Membership Functions into the Perceptron Algorithm","display_name":"Incorporating Fuzzy Membership Functions into the Perceptron Algorithm","publication_year":1985,"publication_date":"1985-11-01","ids":{"openalex":"https://openalex.org/W2165878760","doi":"https://doi.org/10.1109/tpami.1985.4767725","mag":"2165878760","pmid":"https://pubmed.ncbi.nlm.nih.gov/21869307"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1985.4767725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1985.4767725","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5018303984","display_name":"James M. Keller","orcid":"https://orcid.org/0000-0002-0306-7142"},"institutions":[{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James M. Keller","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO 65201","Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO 65201","institution_ids":["https://openalex.org/I76835614"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO, USA","institution_ids":["https://openalex.org/I76835614"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071433731","display_name":"Douglas J. Hunt","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]},{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Douglas J. Hunt","raw_affiliation_strings":["Department of Electrical Engineering, Duke University, Durham, NC, USA","Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO, USA","institution_ids":["https://openalex.org/I76835614"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0865,"has_fulltext":false,"cited_by_count":235,"citation_normalized_percentile":{"value":0.88338192,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"PAMI-7","issue":"6","first_page":"693","last_page":"699"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9955000281333923,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9916999936103821,"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/hyperplane","display_name":"Hyperplane","score":0.6812698841094971},{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.5933418869972229},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5886150598526001},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5809564590454102},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5731726884841919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5224449038505554},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5079274773597717},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.47982358932495117},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46940672397613525},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45844602584838867},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4442077875137329},{"id":"https://openalex.org/keywords/multilayer-perceptron","display_name":"Multilayer perceptron","score":0.43985050916671753},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4007532596588135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36980879306793213},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.22239404916763306}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6812698841094971},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.5933418869972229},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5886150598526001},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5809564590454102},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5731726884841919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5224449038505554},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5079274773597717},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.47982358932495117},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46940672397613525},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45844602584838867},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4442077875137329},{"id":"https://openalex.org/C179717631","wikidata":"https://www.wikidata.org/wiki/Q2991667","display_name":"Multilayer perceptron","level":3,"score":0.43985050916671753},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4007532596588135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36980879306793213},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.22239404916763306},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.1985.4767725","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1985.4767725","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21869307","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21869307","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 pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.699999988079071,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2003892275","https://openalex.org/W2084134149","https://openalex.org/W2113076747","https://openalex.org/W2117156647","https://openalex.org/W4211007335","https://openalex.org/W4400445037"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W2076543106","https://openalex.org/W2331106272","https://openalex.org/W2019891950","https://openalex.org/W2253053392","https://openalex.org/W2085842814","https://openalex.org/W173448675","https://openalex.org/W1531033669","https://openalex.org/W1542808721","https://openalex.org/W1489009679"],"abstract_inverted_index":{"The":[0],"perceptron":[1,58,107],"algorithm,":[2],"one":[3],"of":[4,7,92],"the":[5,35,45,57,67,71,78,87,102,105],"class":[6],"gradient":[8],"descent":[9],"techniques,":[10],"has":[11],"been":[12],"widely":[13],"used":[14],"in":[15,70,86],"pattern":[16],"recognition":[17],"to":[18,28,30,60,104],"determine":[19],"linear":[20],"decision":[21],"boundaries.":[22],"While":[23],"this":[24],"algorithm":[25,59],"is":[26,54,75,96],"guaranteed":[27],"converge":[29],"a":[31,62],"separating":[32],"hyperplane":[33],"if":[34,44],"data":[36,46],"are":[37,47,108],"linearly":[38,49],"separable,":[39],"it":[40],"exhibits":[41],"erratic":[42],"behavior":[43],"not":[48],"separable.":[50],"Fuzzy":[51],"set":[52],"theory":[53],"introduced":[55],"into":[56],"produce":[61],"``fuzzy":[63],"algorithm''":[64],"which":[65],"ameliorates":[66],"convergence":[68],"problem":[69],"nonseparable":[72],"case.":[73,89],"It":[74],"shown":[76],"that":[77],"fuzzy":[79,106],"perceptron,":[80],"like":[81],"its":[82],"crisp":[83,103],"counterpart,":[84],"converges":[85],"separable":[88],"A":[90],"method":[91],"generating":[93],"membership":[94],"functions":[95],"developed,":[97],"and":[98],"experimental":[99],"results":[100],"comparing":[101],"presented.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
