{"id":"https://openalex.org/W4407294446","doi":"https://doi.org/10.3390/axioms14020126","title":"Supervised Learning Fuzzy Matrix Based on Input\u2013Output Fuzzy Vectors","display_name":"Supervised Learning Fuzzy Matrix Based on Input\u2013Output Fuzzy Vectors","publication_year":2025,"publication_date":"2025-02-09","ids":{"openalex":"https://openalex.org/W4407294446","doi":"https://doi.org/10.3390/axioms14020126"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14020126","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020126","pdf_url":"https://www.mdpi.com/2075-1680/14/2/126/pdf?version=1739363214","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/2/126/pdf?version=1739363214","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006543560","display_name":"Meili Ye","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meili Ye","raw_affiliation_strings":["School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025724152","display_name":"Wang Nian-liang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nianliang Wang","raw_affiliation_strings":["School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020419743","display_name":"Xianfeng Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianfeng Yu","raw_affiliation_strings":["School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055190634","display_name":"X. Wang","orcid":"https://orcid.org/0009-0001-0268-9919"},"institutions":[{"id":"https://openalex.org/I4210101072","display_name":"Shangluo University","ror":"https://ror.org/01a56n213","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210101072"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China","institution_ids":["https://openalex.org/I4210101072"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056807499","display_name":"Wuniu Liu","orcid":"https://orcid.org/0000-0002-0220-9436"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wuniu Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710062, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710062, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5056807499"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.3431,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.87749737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"126","last_page":"126"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.8755999803543091,"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":0.8755999803543091,"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":0.850600004196167,"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/T14474","display_name":"Industrial Technology and Control Systems","score":0.8105000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.615350604057312},{"id":"https://openalex.org/keywords/fuzzy-associative-matrix","display_name":"Fuzzy associative matrix","score":0.530722975730896},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5060088038444519},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.46484559774398804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4491552710533142},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3873985707759857},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.3573123514652252},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.3569786548614502},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.060106754302978516}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.615350604057312},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.530722975730896},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5060088038444519},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46484559774398804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4491552710533142},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3873985707759857},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.3573123514652252},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3569786548614502},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.060106754302978516},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14020126","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020126","pdf_url":"https://www.mdpi.com/2075-1680/14/2/126/pdf?version=1739363214","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4acdd4d275cc4a1db9ac194bf99228ab","is_oa":true,"landing_page_url":"https://doaj.org/article/4acdd4d275cc4a1db9ac194bf99228ab","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 2, p 126 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14020126","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14020126","pdf_url":"https://www.mdpi.com/2075-1680/14/2/126/pdf?version=1739363214","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407294446.pdf","grobid_xml":"https://content.openalex.org/works/W4407294446.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W380795639","https://openalex.org/W1494875490","https://openalex.org/W1554018745","https://openalex.org/W2000422349","https://openalex.org/W2003281149","https://openalex.org/W2613648727","https://openalex.org/W3159920741","https://openalex.org/W4211007335","https://openalex.org/W4230588984","https://openalex.org/W4292998656","https://openalex.org/W4294811339","https://openalex.org/W4360596883","https://openalex.org/W4382658016","https://openalex.org/W4385656588","https://openalex.org/W4392104572","https://openalex.org/W4401386638","https://openalex.org/W4403711951","https://openalex.org/W4404238195"],"related_works":["https://openalex.org/W135622916","https://openalex.org/W2118406295","https://openalex.org/W4242970302","https://openalex.org/W2155269963","https://openalex.org/W2571050636","https://openalex.org/W173448675","https://openalex.org/W2331106272","https://openalex.org/W2155210646","https://openalex.org/W2128391754","https://openalex.org/W2151351600"],"abstract_inverted_index":{"Fuzzy":[0],"matrices":[1,21],"play":[2],"a":[3,89],"crucial":[4],"role":[5],"in":[6],"fuzzy":[7,10,20,27,31],"logic":[8],"and":[9,64,113],"systems.":[11],"This":[12],"paper":[13],"investigates":[14],"the":[15,30,38,60,68,76,82,85,106],"problem":[16],"of":[17,25,84],"supervised":[18],"learning":[19,111],"through":[22],"sample":[23],"pairs":[24],"input\u2013output":[26,119],"vectors,":[28],"where":[29],"matrix":[32,69],"inference":[33],"mechanism":[34],"is":[35,95],"based":[36,47],"on":[37,48,67],"max\u2013min":[39,86,94],"composition":[40,87],"method.":[41],"We":[42],"propose":[43],"an":[44,55],"optimization":[45],"approach":[46],"stochastic":[49],"gradient":[50],"descent":[51],"(SGD),":[52],"which":[53],"defines":[54],"objective":[56],"function":[57,92],"by":[58],"using":[59],"mean":[61],"squared":[62],"error":[63],"incorporates":[65],"constraints":[66],"elements":[70],"(ensuring":[71],"they":[72],"take":[73],"values":[74],"within":[75],"interval":[77],"[0,":[78],"1]).":[79],"To":[80],"address":[81],"non-smoothness":[83],"rule,":[88],"modified":[90],"smoothing":[91],"for":[93],"employed,":[96],"ensuring":[97],"stability":[98],"during":[99],"optimization.":[100],"The":[101],"experimental":[102],"results":[103],"demonstrate":[104],"that":[105],"proposed":[107],"method":[108],"achieves":[109],"high":[110],"accuracy":[112],"convergence":[114],"across":[115],"multiple":[116],"randomly":[117],"generated":[118],"vector":[120],"samples.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
