{"id":"https://openalex.org/W1600426049","doi":"https://doi.org/10.1007/11427391_6","title":"On the Universal Approximation Theorem of Fuzzy Neural Networks with Random Membership Function Parameters","display_name":"On the Universal Approximation Theorem of Fuzzy Neural Networks with Random Membership Function Parameters","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1600426049","doi":"https://doi.org/10.1007/11427391_6","mag":"1600426049"},"language":"en","primary_location":{"id":"doi:10.1007/11427391_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11427391_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5086764741","display_name":"Lipo Wang","orcid":"https://orcid.org/0000-0002-4257-7639"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["CN","SG"],"is_corresponding":true,"raw_author_name":"Lipo Wang","raw_affiliation_strings":["College of Information Engineering, Xiangtan University, Xiangtan, Hunan, China","School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering, Xiangtan University, Xiangtan, Hunan, China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109831307","display_name":"Bing Liu","orcid":"https://orcid.org/0000-0003-2029-5187"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Bing Liu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102149142","display_name":"Chunru Wan","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Chunru Wan","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technology University, Block S1, 50 Nanyang Avenue, 639798, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086764741"],"corresponding_institution_ids":["https://openalex.org/I172675005","https://openalex.org/I4610292"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.9972,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77308683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"45","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"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/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"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":0.9987999796867371,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9570000171661377,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7201657295227051},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6968883872032166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6236509084701538},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6077399849891663},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.48394349217414856},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46264755725860596},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.44962579011917114},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4491536021232605},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.44773054122924805},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43165671825408936},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.43089112639427185},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4287189245223999},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4157427251338959},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3316129446029663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31526291370391846},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.26542505621910095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09432271122932434}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7201657295227051},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6968883872032166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6236509084701538},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6077399849891663},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.48394349217414856},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46264755725860596},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.44962579011917114},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4491536021232605},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.44773054122924805},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43165671825408936},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.43089112639427185},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4287189245223999},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4157427251338959},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3316129446029663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31526291370391846},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26542505621910095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09432271122932434},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11427391_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11427391_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W115420483","https://openalex.org/W203904786","https://openalex.org/W1486579091","https://openalex.org/W1500731913","https://openalex.org/W1613269347","https://openalex.org/W1731748326","https://openalex.org/W1833345539","https://openalex.org/W2019207321","https://openalex.org/W2034637379","https://openalex.org/W2054902599","https://openalex.org/W2077937929","https://openalex.org/W2103414828","https://openalex.org/W2142544077","https://openalex.org/W2151419026","https://openalex.org/W2152853212","https://openalex.org/W2153904408","https://openalex.org/W2155530550","https://openalex.org/W3146863510","https://openalex.org/W4205303537"],"related_works":["https://openalex.org/W4236695056","https://openalex.org/W87675884","https://openalex.org/W154406135","https://openalex.org/W2132859092","https://openalex.org/W2320922716","https://openalex.org/W2013143463","https://openalex.org/W2384503959","https://openalex.org/W2181335288","https://openalex.org/W2012019755","https://openalex.org/W2374152511"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}