{"id":"https://openalex.org/W2067764192","doi":"https://doi.org/10.1109/tfuzz.2013.2239649","title":"A Note on Fuzzy Relational Equations With Min-Implication Composition","display_name":"A Note on Fuzzy Relational Equations With Min-Implication Composition","publication_year":2013,"publication_date":"2013-01-11","ids":{"openalex":"https://openalex.org/W2067764192","doi":"https://doi.org/10.1109/tfuzz.2013.2239649","mag":"2067764192"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2013.2239649","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2239649","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Fuzzy Systems","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/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Pingke Li","raw_affiliation_strings":["Department of Industrial Engineering, Tsinghua University, Beijing, China","Dept. of Ind. Eng., Tsinghua Univ., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Dept. of Ind. Eng., Tsinghua Univ., Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013548183"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.32839027,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66412021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"5","first_page":"983","last_page":"986"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9970999956130981,"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":0.9970999956130981,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.992900013923645,"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/T11106","display_name":"Data Management and Algorithms","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/solution-set","display_name":"Solution set","score":0.7589902877807617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7470132112503052},{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.6172542572021484},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5798128843307495},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5486867427825928},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5045117139816284},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.496008962392807},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4566868543624878},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43224525451660156},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.4308960437774658},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4165896475315094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38201242685317993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20933327078819275},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18051669001579285}],"concepts":[{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.7589902877807617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7470132112503052},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.6172542572021484},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5798128843307495},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5486867427825928},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5045117139816284},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.496008962392807},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4566868543624878},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43224525451660156},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.4308960437774658},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4165896475315094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38201242685317993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20933327078819275},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18051669001579285},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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:10.1109/tfuzz.2013.2239649","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2239649","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Fuzzy Systems","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":23,"referenced_works":["https://openalex.org/W20275348","https://openalex.org/W127405698","https://openalex.org/W294994052","https://openalex.org/W657218221","https://openalex.org/W1521951439","https://openalex.org/W1975873416","https://openalex.org/W1976127067","https://openalex.org/W1980775764","https://openalex.org/W1987437333","https://openalex.org/W2009106360","https://openalex.org/W2012628629","https://openalex.org/W2017831479","https://openalex.org/W2038907829","https://openalex.org/W2044684553","https://openalex.org/W2047838564","https://openalex.org/W2054726552","https://openalex.org/W2061821032","https://openalex.org/W2080947358","https://openalex.org/W2087871163","https://openalex.org/W2090700466","https://openalex.org/W2159441390","https://openalex.org/W2161541700","https://openalex.org/W2323334529"],"related_works":["https://openalex.org/W4376608589","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W3008555607","https://openalex.org/W2895486115","https://openalex.org/W2506892714","https://openalex.org/W201115563","https://openalex.org/W2742830016","https://openalex.org/W2060558425","https://openalex.org/W2189146502"],"abstract_inverted_index":{"The":[0,23],"fuzzy":[1,53],"relational":[2,54],"equations":[3,55],"with":[4,17,56],"min-implication":[5,57],"composition":[6,58],"are":[7,115],"considered,":[8],"where":[9],"the":[10,15,20,76,94,104],"implication":[11],"operation":[12],"involved":[13],"is":[14,47,91,100],"residuum":[16],"respect":[18],"to":[19,103],"minimum":[21,39],"operation.":[22],"solution":[24,40,80],"set":[25,81],"of":[26,30,52,68,78,96,109],"such":[27],"a":[28,38,50,66,86],"system":[29,51,67],"equations,":[31],"whenever":[32],"nonempty,":[33],"can":[34,59,82],"be":[35,60,83],"characterized":[36],"by":[37],"and":[41,74],"finitely":[42],"many":[43],"maximal":[44,98],"solutions.":[45],"It":[46],"shown":[48,92],"that":[49,93],"reformulated":[61],"in":[62,85],"polynomial":[63],"time":[64],"into":[65],"0-1":[69],"mixed":[70],"integer":[71],"linear":[72],"inequalities,":[73],"consequently,":[75],"structure":[77],"its":[79],"revealed":[84],"succinct":[87],"manner.":[88],"Besides,":[89],"it":[90],"determination":[95],"all":[97],"solutions":[99],"polynomially":[101],"reducible":[102],"transversal":[105],"hypergraph":[106],"generation":[107],"problem,":[108],"which":[110],"some":[111],"practically":[112],"well-performed":[113],"algorithms":[114],"available.":[116]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}