{"id":"https://openalex.org/W2050028634","doi":"https://doi.org/10.1109/fuzzy.2006.1681976","title":"On an Approximate-inclusion-based Difference Operator - Application to the Division of Fuzzy Relations","display_name":"On an Approximate-inclusion-based Difference Operator - Application to the Division of Fuzzy Relations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2050028634","doi":"https://doi.org/10.1109/fuzzy.2006.1681976","mag":"2050028634"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2006.1681976","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2006.1681976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE 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/A5111972319","display_name":"P. Bosc","orcid":null},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Bosc","raw_affiliation_strings":["Irisa-Enssat, Lannion"],"affiliations":[{"raw_affiliation_string":"Irisa-Enssat, Lannion","institution_ids":["https://openalex.org/I2802519937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055310601","display_name":"Olivier Pivert","orcid":"https://orcid.org/0000-0003-4103-5819"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"O. Pivert","raw_affiliation_strings":["IRISA-ENSSAT","IRISA-ENSSAT, Lannion, France"],"affiliations":[{"raw_affiliation_string":"IRISA-ENSSAT","institution_ids":["https://openalex.org/I2802519937"]},{"raw_affiliation_string":"IRISA-ENSSAT, Lannion, France","institution_ids":["https://openalex.org/I2802519937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111972319"],"corresponding_institution_ids":["https://openalex.org/I2802519937"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12106953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"1988","last_page":"1995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9973999857902527,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9951000213623047,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9890000224113464,"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/inclusion","display_name":"Inclusion (mineral)","score":0.7650562524795532},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.7406694293022156},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.5868292450904846},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5702469348907471},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5414493083953857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5247290730476379},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5247278809547424},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.48839467763900757},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.466386079788208},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4498882293701172},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4144923686981201},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3851384222507477},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3537091612815857},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3446164131164551},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33875250816345215},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.16320395469665527},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16060012578964233},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1373485028743744},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09883078932762146},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09036311507225037},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07542818784713745}],"concepts":[{"id":"https://openalex.org/C109359841","wikidata":"https://www.wikidata.org/wiki/Q728944","display_name":"Inclusion (mineral)","level":2,"score":0.7650562524795532},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.7406694293022156},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.5868292450904846},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5702469348907471},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5414493083953857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5247290730476379},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5247278809547424},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.48839467763900757},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.466386079788208},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4498882293701172},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4144923686981201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3851384222507477},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3537091612815857},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3446164131164551},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33875250816345215},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16320395469665527},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16060012578964233},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1373485028743744},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09883078932762146},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09036311507225037},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07542818784713745},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2006.1681976","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2006.1681976","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W100355504","https://openalex.org/W189366404","https://openalex.org/W1552993212","https://openalex.org/W1980080444","https://openalex.org/W1981072245","https://openalex.org/W2001910480","https://openalex.org/W2017695773","https://openalex.org/W2069656851","https://openalex.org/W2123474039","https://openalex.org/W2139587137","https://openalex.org/W2141265681","https://openalex.org/W6633171403"],"related_works":["https://openalex.org/W2120204135","https://openalex.org/W1796293478","https://openalex.org/W174435416","https://openalex.org/W2168276503","https://openalex.org/W2139396251","https://openalex.org/W1577544887","https://openalex.org/W1573537275","https://openalex.org/W2047973569","https://openalex.org/W1993884761","https://openalex.org/W2553821524"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,31,43,70,83],"devoted":[3],"to":[4,71],"the":[5,16,46,49,86,91,94,98],"definition":[6],"of":[7,15,21,29,35,39,48,88,93,97,101],"a":[8,13,33,60,64],"difference":[9],"operator":[10],"founded":[11],"on":[12,45],"relaxation":[14],"inclusion.":[17],"The":[18,37],"regular":[19],"inclusion":[20,42,62],"A":[22,30],"in":[23,80,85],"B":[24],"entails":[25],"that":[26,58],"any":[27],"element":[28],"also":[32],"member":[34],"B.":[36],"concept":[38],"an":[40],"approximate":[41],"based":[44],"softening":[47],"universal":[50],"quantifier":[51],"(all)":[52],"into":[53],"\"almost":[54],"all\".":[55],"We":[56],"show":[57],"such":[59],"weakened":[61],"induces":[63],"drastic":[65],"difference,":[66],"whose":[67],"main":[68],"characteristics":[69],"be":[72,78],"non-deterministic.":[73],"Despite":[74],"this,":[75],"it":[76],"can":[77],"used":[79],"practice,":[81],"which":[82],"illustrated":[84],"area":[87],"databases,":[89],"with":[90],"question":[92],"algebraic":[95],"rewriting":[96],"(approximate)":[99],"division":[100],"relations.":[102]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}