{"id":"https://openalex.org/W2159441390","doi":"https://doi.org/10.1007/s10700-009-9059-0","title":"A survey on fuzzy relational equations, part I: classification and solvability","display_name":"A survey on fuzzy relational equations, part I: classification and solvability","publication_year":2009,"publication_date":"2009-03-28","ids":{"openalex":"https://openalex.org/W2159441390","doi":"https://doi.org/10.1007/s10700-009-9059-0","mag":"2159441390"},"language":"en","primary_location":{"id":"doi:10.1007/s10700-009-9059-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-009-9059-0","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","raw_type":"journal-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/A5013548183","display_name":"Pingke Li","orcid":"https://orcid.org/0000-0003-2244-3139"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pingke Li","raw_affiliation_strings":["Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027860626","display_name":"Shu\u2010Cherng Fang","orcid":"https://orcid.org/0000-0001-5087-3262"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shu-Cherng Fang","raw_affiliation_strings":["Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013548183"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":{"value":2590,"currency":"EUR","value_usd":3390},"apc_paid":null,"fwci":11.7463,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.98622055,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":"2","first_page":"179","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9980000257492065,"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":0.9980000257492065,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9894000291824341,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.5952869057655334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5089142322540283},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4418225884437561},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39433830976486206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3700753450393677},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.34806668758392334}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5952869057655334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5089142322540283},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4418225884437561},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39433830976486206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3700753450393677},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34806668758392334}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10700-009-9059-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-009-9059-0","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":261,"referenced_works":["https://openalex.org/W4193965","https://openalex.org/W16272443","https://openalex.org/W26772505","https://openalex.org/W40013532","https://openalex.org/W49782344","https://openalex.org/W76313619","https://openalex.org/W87906459","https://openalex.org/W88494277","https://openalex.org/W92944258","https://openalex.org/W98520975","https://openalex.org/W122093954","https://openalex.org/W127405698","https://openalex.org/W139983096","https://openalex.org/W145213067","https://openalex.org/W148465446","https://openalex.org/W148896681","https://openalex.org/W161157074","https://openalex.org/W170294950","https://openalex.org/W198763519","https://openalex.org/W294994052","https://openalex.org/W352516286","https://openalex.org/W377680676","https://openalex.org/W382834063","https://openalex.org/W409549338","https://openalex.org/W567518060","https://openalex.org/W580985703","https://openalex.org/W586748284","https://openalex.org/W590777244","https://openalex.org/W615011212","https://openalex.org/W615136929","https://openalex.org/W618244563","https://openalex.org/W621724833","https://openalex.org/W623232919","https://openalex.org/W657218221","https://openalex.org/W1485625483","https://openalex.org/W1492076504","https://openalex.org/W1500295365","https://openalex.org/W1500352601","https://openalex.org/W1508373211","https://openalex.org/W1509335165","https://openalex.org/W1554822239","https://openalex.org/W1557235141","https://openalex.org/W1569419053","https://openalex.org/W1570082825","https://openalex.org/W1585300236","https://openalex.org/W1588115473","https://openalex.org/W1600267829","https://openalex.org/W1600302332","https://openalex.org/W1603455683","https://openalex.org/W1606982009","https://openalex.org/W1777706652","https://openalex.org/W1871175145","https://openalex.org/W1892058798","https://openalex.org/W1898259180","https://openalex.org/W1938153123","https://openalex.org/W1967309842","https://openalex.org/W1969263569","https://openalex.org/W1970415313","https://openalex.org/W1970998538","https://openalex.org/W1971016194","https://openalex.org/W1971165057","https://openalex.org/W1973167345","https://openalex.org/W1974453514","https://openalex.org/W1975147658","https://openalex.org/W1977000157","https://openalex.org/W1978471043","https://openalex.org/W1980090346","https://openalex.org/W1980564456","https://openalex.org/W1981342016","https://openalex.org/W1981490287","https://openalex.org/W1982657605","https://openalex.org/W1983256028","https://openalex.org/W1985403939","https://openalex.org/W1988799725","https://openalex.org/W1989114736","https://openalex.org/W1989512364","https://openalex.org/W1990360647","https://openalex.org/W1990673965","https://openalex.org/W1991241876","https://openalex.org/W1991466857","https://openalex.org/W1991475392","https://openalex.org/W1991602864","https://openalex.org/W1991608514","https://openalex.org/W1991767164","https://openalex.org/W1993333092","https://openalex.org/W1993810822","https://openalex.org/W1994893702","https://openalex.org/W1995151750","https://openalex.org/W1995638481","https://openalex.org/W1996003707","https://openalex.org/W1996212544","https://openalex.org/W1996486820","https://openalex.org/W1997412469","https://openalex.org/W1997511955","https://openalex.org/W1998169032","https://openalex.org/W2002955598","https://openalex.org/W2003105385","https://openalex.org/W2003364577","https://openalex.org/W2009106360","https://openalex.org/W2010276308","https://openalex.org/W2010548783","https://openalex.org/W2010929656","https://openalex.org/W2011109283","https://openalex.org/W2011184387","https://openalex.org/W2011938136","https://openalex.org/W2012201562","https://openalex.org/W2013582830","https://openalex.org/W2014430014","https://openalex.org/W2014734381","https://openalex.org/W2016951714","https://openalex.org/W2017703673","https://openalex.org/W2018323950","https://openalex.org/W2018699878","https://openalex.org/W2019716713","https://openalex.org/W2019901578","https://openalex.org/W2021027318","https://openalex.org/W2021755310","https://openalex.org/W2022011877","https://openalex.org/W2022923512","https://openalex.org/W2023536261","https://openalex.org/W2025021415","https://openalex.org/W2026126632","https://openalex.org/W2026360850","https://openalex.org/W2026370233","https://openalex.org/W2026457244","https://openalex.org/W2026480595","https://openalex.org/W2026781292","https://openalex.org/W2028482837","https://openalex.org/W2029407995","https://openalex.org/W2029795273","https://openalex.org/W2030229879","https://openalex.org/W2031345712","https://openalex.org/W2031883508","https://openalex.org/W2033869664","https://openalex.org/W2035096056","https://openalex.org/W2036338807","https://openalex.org/W2036460158","https://openalex.org/W2036566620","https://openalex.org/W2038907829","https://openalex.org/W2039487266","https://openalex.org/W2039623063","https://openalex.org/W2039921144","https://openalex.org/W2040513729","https://openalex.org/W2040566590","https://openalex.org/W2041180721","https://openalex.org/W2042025428","https://openalex.org/W2043555242","https://openalex.org/W2044636175","https://openalex.org/W2044684553","https://openalex.org/W2045266559","https://openalex.org/W2045459931","https://openalex.org/W2045586868","https://openalex.org/W2045667604","https://openalex.org/W2046701989","https://openalex.org/W2048790809","https://openalex.org/W2049785322","https://openalex.org/W2050412337","https://openalex.org/W2051106936","https://openalex.org/W2051272855","https://openalex.org/W2051818124","https://openalex.org/W2052326481","https://openalex.org/W2054416947","https://openalex.org/W2054726552","https://openalex.org/W2055681799","https://openalex.org/W2058125275","https://openalex.org/W2058416216","https://openalex.org/W2058553681","https://openalex.org/W2059287801","https://openalex.org/W2059994445","https://openalex.org/W2061821032","https://openalex.org/W2062411905","https://openalex.org/W2062636177","https://openalex.org/W2063937398","https://openalex.org/W2065397160","https://openalex.org/W2067259779","https://openalex.org/W2069593643","https://openalex.org/W2069687967","https://openalex.org/W2070253848","https://openalex.org/W2073233659","https://openalex.org/W2073491228","https://openalex.org/W2074412285","https://openalex.org/W2075826824","https://openalex.org/W2076186876","https://openalex.org/W2078306763","https://openalex.org/W2082392923","https://openalex.org/W2083388788","https://openalex.org/W2086412078","https://openalex.org/W2086624093","https://openalex.org/W2087349227","https://openalex.org/W2087871163","https://openalex.org/W2090700466","https://openalex.org/W2091882643","https://openalex.org/W2092179943","https://openalex.org/W2092203888","https://openalex.org/W2093026734","https://openalex.org/W2093075287","https://openalex.org/W2093397547","https://openalex.org/W2094360224","https://openalex.org/W2094487054","https://openalex.org/W2095108035","https://openalex.org/W2096071080","https://openalex.org/W2101142565","https://openalex.org/W2107551402","https://openalex.org/W2112371487","https://openalex.org/W2112660043","https://openalex.org/W2113250809","https://openalex.org/W2113720027","https://openalex.org/W2118125151","https://openalex.org/W2120397231","https://openalex.org/W2123741539","https://openalex.org/W2128160792","https://openalex.org/W2128444310","https://openalex.org/W2130574265","https://openalex.org/W2131429285","https://openalex.org/W2134194719","https://openalex.org/W2134718370","https://openalex.org/W2135949973","https://openalex.org/W2136069469","https://openalex.org/W2139654996","https://openalex.org/W2142620692","https://openalex.org/W2148634357","https://openalex.org/W2155096631","https://openalex.org/W2157041604","https://openalex.org/W2167802269","https://openalex.org/W2181281907","https://openalex.org/W2199004907","https://openalex.org/W2199514203","https://openalex.org/W2407978271","https://openalex.org/W2489872647","https://openalex.org/W2495730988","https://openalex.org/W2496338429","https://openalex.org/W2511330549","https://openalex.org/W2538995836","https://openalex.org/W2576345399","https://openalex.org/W2578456536","https://openalex.org/W2581517321","https://openalex.org/W2589041627","https://openalex.org/W2616337127","https://openalex.org/W2616791547","https://openalex.org/W2621795486","https://openalex.org/W2633656933","https://openalex.org/W2746933270","https://openalex.org/W2889749418","https://openalex.org/W2911632998","https://openalex.org/W2912565176","https://openalex.org/W2969808124","https://openalex.org/W3213572188","https://openalex.org/W4205912702","https://openalex.org/W4211007335","https://openalex.org/W4234106517","https://openalex.org/W4234672050","https://openalex.org/W4236125843","https://openalex.org/W4241764762","https://openalex.org/W4245152641","https://openalex.org/W4255390256","https://openalex.org/W4255417137","https://openalex.org/W4292295629","https://openalex.org/W4299417699","https://openalex.org/W4300680636","https://openalex.org/W6635908788","https://openalex.org/W6645451138"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2033914206","https://openalex.org/W2042327336"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}