{"id":"https://openalex.org/W2131691211","doi":"https://doi.org/10.1109/fuzzy.2010.5584682","title":"Non-negative matrix factorization and decomposition of a fuzzy relation","display_name":"Non-negative matrix factorization and decomposition of a fuzzy relation","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2131691211","doi":"https://doi.org/10.1109/fuzzy.2010.5584682","mag":"2131691211"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2010.5584682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2010.5584682","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference on Fuzzy Systems","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/A5111445543","display_name":"Barnab\u00e1s Bede","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Barnabas Bede","raw_affiliation_strings":["Department of Mathematics, University of Texas-Pan American, Edinburgh, TX, UK","Department of Mathematics, The University of Texas-Pan American, Edinburg, TX, 78541, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas-Pan American, Edinburgh, TX, UK","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, The University of Texas-Pan American, Edinburg, TX, 78541, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085264826","display_name":"Hajime Nobuhara","orcid":"https://orcid.org/0000-0002-1818-6929"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hajime Nobuhara","raw_affiliation_strings":["Department of Intelligent Interaction Technologies, University of Tsukuba, Tsukuba, Ibaraki, Japan","Dept. of Intelligent Interaction Technologies, University of Tsukuba, Tenoudai 1-1-1Tsukuba City Ibaraki 305-8573 Japan"],"affiliations":[{"raw_affiliation_string":"Department of Intelligent Interaction Technologies, University of Tsukuba, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Dept. of Intelligent Interaction Technologies, University of Tsukuba, Tenoudai 1-1-1Tsukuba City Ibaraki 305-8573 Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010869153","display_name":"Imre J. Rudas","orcid":"https://orcid.org/0000-0002-2067-8578"},"institutions":[{"id":"https://openalex.org/I103356709","display_name":"Obuda University","ror":"https://ror.org/00ax71d21","country_code":"HU","type":"education","lineage":["https://openalex.org/I103356709"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Imre J. Rudas","raw_affiliation_strings":["\u00d3buda University, Budapest, Hungary","Obuda University, Be\u00b4csi u\u00b4t 96/B, H-1034, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"\u00d3buda University, Budapest, Hungary","institution_ids":["https://openalex.org/I103356709"]},{"raw_affiliation_string":"Obuda University, Be\u00b4csi u\u00b4t 96/B, H-1034, Budapest, Hungary","institution_ids":["https://openalex.org/I103356709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063318523","display_name":"Takanari Tanabata","orcid":null},"institutions":[{"id":"https://openalex.org/I3018761593","display_name":"Institute of Agrobiological Sciences","ror":"https://ror.org/01786mp71","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1323638106","https://openalex.org/I3018761593"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takanari Tanabata","raw_affiliation_strings":["National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan","National Institute of Agrobiological Sciences, 2-1-2, Kannondai, Tsukuba, Ibaraki, 305-8602, Japan"],"affiliations":[{"raw_affiliation_string":"National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I3018761593"]},{"raw_affiliation_string":"National Institute of Agrobiological Sciences, 2-1-2, Kannondai, Tsukuba, Ibaraki, 305-8602, Japan","institution_ids":["https://openalex.org/I3018761593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111445543"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14093785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"401","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9904000163078308,"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":0.9904000163078308,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9897000193595886,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.7265224456787109},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6351293921470642},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6129021644592285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6049627065658569},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5487297177314758},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5421602725982666},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.5216070413589478},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5199583768844604},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.517997145652771},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.5081024169921875},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46677273511886597},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4410296678543091},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3357635736465454},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2962478995323181},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2769608497619629},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24322670698165894},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1268315315246582},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06780466437339783},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05373513698577881}],"concepts":[{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.7265224456787109},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6351293921470642},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6129021644592285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6049627065658569},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5487297177314758},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5421602725982666},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.5216070413589478},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5199583768844604},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.517997145652771},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.5081024169921875},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46677273511886597},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4410296678543091},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3357635736465454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2962478995323181},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2769608497619629},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24322670698165894},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1268315315246582},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06780466437339783},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05373513698577881},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/fuzzy.2010.5584682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2010.5584682","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W657218221","https://openalex.org/W1535408272","https://openalex.org/W1902027874","https://openalex.org/W1976391658","https://openalex.org/W1982140226","https://openalex.org/W2009276485","https://openalex.org/W2013655648","https://openalex.org/W2017288758","https://openalex.org/W2135029798","https://openalex.org/W2137807761","https://openalex.org/W2808650095","https://openalex.org/W2907435879","https://openalex.org/W3143596294","https://openalex.org/W6680012447"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840"],"abstract_inverted_index":{"The":[0],"present":[1],"paper":[2],"generalizes":[3],"the":[4],"problems":[5],"of":[6,12,38],"nonnegative":[7],"matrix":[8,20],"factorization":[9,21],"and":[10],"decomposition":[11],"fuzzy":[13],"relation":[14],"into":[15],"a":[16,27],"common":[17],"non-linear":[18],"non-negative":[19],"problem.":[22],"Algorithms":[23],"for":[24],"solving":[25],"such":[26],"general":[28,35],"nonlinear":[29],"problem":[30],"are":[31,50],"discussed,":[32],"based":[33],"on":[34],"algebraic":[36],"structures":[37],"ordered":[39],"semirings":[40],"with":[41],"generated":[42],"pseudo-operations.":[43],"Some":[44],"decompositions":[45],"in":[46],"max-product,":[47],"max-plus":[48],"algebras":[49],"also":[51],"shown.":[52]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}