{"id":"https://openalex.org/W2515481001","doi":"https://doi.org/10.1109/tfuzz.2016.2598860","title":"Do We Need Minimal Solutions of Fuzzy Relational Equations in Advance?","display_name":"Do We Need Minimal Solutions of Fuzzy Relational Equations in Advance?","publication_year":2016,"publication_date":"2016-08-10","ids":{"openalex":"https://openalex.org/W2515481001","doi":"https://doi.org/10.1109/tfuzz.2016.2598860","mag":"2515481001"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2016.2598860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2598860","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/A5027925658","display_name":"Eduard Bartl","orcid":"https://orcid.org/0000-0002-1273-0268"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Eduard Bartl","raw_affiliation_strings":["Department of Computer Science, Palack\u00fd University Olomouc, Olomouc, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Palack\u00fd University Olomouc, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102974778","display_name":"Pavel Proch\u00e1zka","orcid":"https://orcid.org/0000-0001-7456-3322"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Pavel Prochazka","raw_affiliation_strings":["Department of Computer Science, Palack\u00fd University Olomouc, Olomouc, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Palack\u00fd University Olomouc, Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027925658"],"corresponding_institution_ids":["https://openalex.org/I70703428"],"apc_list":null,"apc_paid":null,"fwci":0.8569,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83959104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"5","first_page":"1356","last_page":"1363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.996999979019165,"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":0.996999979019165,"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":0.9883999824523926,"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":0.980400025844574,"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/solution-set","display_name":"Solution set","score":0.7332162857055664},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6916885375976562},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6504538059234619},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.6309491991996765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5790824294090271},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5500581860542297},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5445561408996582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4078959822654724},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36620986461639404},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3451725244522095},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3277737498283386},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20889651775360107},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1356641948223114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09628835320472717}],"concepts":[{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.7332162857055664},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6916885375976562},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6504538059234619},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.6309491991996765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5790824294090271},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5500581860542297},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5445561408996582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4078959822654724},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36620986461639404},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3451725244522095},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3277737498283386},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20889651775360107},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1356641948223114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09628835320472717},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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.2016.2598860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2016.2598860","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.75}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W127405698","https://openalex.org/W1598508750","https://openalex.org/W1714045541","https://openalex.org/W1973571761","https://openalex.org/W1976430007","https://openalex.org/W1984314602","https://openalex.org/W1987437333","https://openalex.org/W1990673965","https://openalex.org/W1991764565","https://openalex.org/W1993012978","https://openalex.org/W1997100226","https://openalex.org/W2005441399","https://openalex.org/W2029338278","https://openalex.org/W2039904522","https://openalex.org/W2042960352","https://openalex.org/W2044935944","https://openalex.org/W2046250921","https://openalex.org/W2047838564","https://openalex.org/W2061821032","https://openalex.org/W2063292248","https://openalex.org/W2078846431","https://openalex.org/W2082911118","https://openalex.org/W2093863186","https://openalex.org/W2097834100","https://openalex.org/W2099459744","https://openalex.org/W2110182592","https://openalex.org/W2154274300","https://openalex.org/W2159441390","https://openalex.org/W2496338429","https://openalex.org/W2506954980","https://openalex.org/W2579555219","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2912565176","https://openalex.org/W4205471131","https://openalex.org/W4211007335","https://openalex.org/W4213427446","https://openalex.org/W4254807835","https://openalex.org/W4403297636","https://openalex.org/W6635757092","https://openalex.org/W6674792682","https://openalex.org/W6872573746","https://openalex.org/W7047544994"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W2006389905","https://openalex.org/W2296389180"],"abstract_inverted_index":{"Minimal":[0],"solutions":[1,10,21,98],"play":[2],"a":[3,12,23,45],"crucial":[4],"role":[5],"in":[6,99],"description":[7],"of":[8,47,83,93],"all":[9,20,34,95],"to":[11,28,106],"fuzzy":[13],"relational":[14],"equation.":[15],"The":[16,73],"reason":[17],"is":[18,76],"that":[19],"form":[22],"convex":[24],"set":[25,30,43],"with":[26],"respect":[27],"(fuzzy)":[29],"inclusion;":[31],"therefore,":[32],"having":[33,94],"extremal":[35],"solutions,":[36],"we":[37,68],"can":[38],"represent":[39],"the":[40,53,60,66,85,91,96,103],"entire":[41],"solution":[42,55,86],"as":[44,77],"union":[46],"intervals":[48],"bounded":[49],"from":[50,57],"above":[51],"by":[52,59],"greatest":[54],"and":[56],"below":[58],"minimal":[61,97],"solutions.":[62,72],"However,":[63],"when":[64],"computing":[65],"intervals,":[67],"obtain":[69],"many":[70],"duplicate":[71],"obvious":[74],"question":[75],"follows:":[78],"Is":[79],"there":[80],"another":[81],"way":[82],"representing":[84],"set,":[87],"for":[88],"instance,":[89],"without":[90],"need":[92],"advance?":[100],"We":[101],"provide":[102],"positive":[104],"answer":[105],"this":[107],"question.":[108]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}