{"id":"https://openalex.org/W2005174759","doi":"https://doi.org/10.1080/03081070290005186","title":"Reducing t-norms and augmenting t-conorms","display_name":"Reducing t-norms and augmenting t-conorms","publication_year":2002,"publication_date":"2002-05-01","ids":{"openalex":"https://openalex.org/W2005174759","doi":"https://doi.org/10.1080/03081070290005186","mag":"2005174759"},"language":"en","primary_location":{"id":"doi:10.1080/03081070290005186","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081070290005186","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General 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/A5065404842","display_name":"Marcin Detyniecki","orcid":"https://orcid.org/0000-0001-5669-4871"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marcin Detyniecki","raw_affiliation_strings":["LIP6-CNRS , University of Paris VI , 4, place Jussieu, Paris Cedex 05, 75230, France"],"affiliations":[{"raw_affiliation_string":"LIP6-CNRS , University of Paris VI , 4, place Jussieu, Paris Cedex 05, 75230, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072431554","display_name":"Ronald R. Yager","orcid":"https://orcid.org/0000-0003-2938-1858"},"institutions":[{"id":"https://openalex.org/I173466955","display_name":"Iona College","ror":"https://ror.org/00m79dm66","country_code":"US","type":"education","lineage":["https://openalex.org/I173466955"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald R. Yager","raw_affiliation_strings":["Machine Intelligence Institute , Iona College , New Rochelle, NY, 10801, USA","Machine Intelligence Institute, Iona College,New Rochelle, NY 10801, USA"],"affiliations":[{"raw_affiliation_string":"Machine Intelligence Institute , Iona College , New Rochelle, NY, 10801, USA","institution_ids":["https://openalex.org/I173466955"]},{"raw_affiliation_string":"Machine Intelligence Institute, Iona College,New Rochelle, NY 10801, USA","institution_ids":["https://openalex.org/I173466955"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107338358","display_name":"Bernadette Bouchon\u2010Meunier","orcid":"https://orcid.org/0000-0002-7937-7796"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernadette Bouchon-Meunier","raw_affiliation_strings":["LIP6-CNRS , University of Paris VI , 4, place Jussieu, Paris Cedex 05, 75230, France"],"affiliations":[{"raw_affiliation_string":"LIP6-CNRS , University of Paris VI , 4, place Jussieu, Paris Cedex 05, 75230, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065404842"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.4467,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65865555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"3","first_page":"265","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9934999942779541,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8212509751319885},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.728439211845398},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6148182153701782},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6136637330055237},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4843538999557495},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.4236219525337219},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.41504818201065063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40788331627845764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3521876633167267},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33259889483451843},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21712490916252136},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13287609815597534},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.12156715989112854},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.08805814385414124},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.07882976531982422}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8212509751319885},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.728439211845398},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6148182153701782},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6136637330055237},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4843538999557495},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.4236219525337219},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.41504818201065063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40788331627845764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3521876633167267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33259889483451843},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21712490916252136},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13287609815597534},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.12156715989112854},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.08805814385414124},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.07882976531982422},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03081070290005186","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081070290005186","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General 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":24,"referenced_works":["https://openalex.org/W16259239","https://openalex.org/W1485625483","https://openalex.org/W1495481456","https://openalex.org/W1570082825","https://openalex.org/W1881814505","https://openalex.org/W1964679164","https://openalex.org/W1968172834","https://openalex.org/W1990794890","https://openalex.org/W2020391927","https://openalex.org/W2024647450","https://openalex.org/W2048288497","https://openalex.org/W2059245341","https://openalex.org/W2062633196","https://openalex.org/W2164429865","https://openalex.org/W2174826014","https://openalex.org/W2578456536","https://openalex.org/W2782519984","https://openalex.org/W2911855504","https://openalex.org/W3043771091","https://openalex.org/W3158113069","https://openalex.org/W3213572188","https://openalex.org/W4234672050","https://openalex.org/W6607659909","https://openalex.org/W6856745558"],"related_works":["https://openalex.org/W2374649169","https://openalex.org/W2023111059","https://openalex.org/W2101854716","https://openalex.org/W3184166521","https://openalex.org/W4386164526","https://openalex.org/W1533671261","https://openalex.org/W2048205257","https://openalex.org/W2142575742","https://openalex.org/W2187531049","https://openalex.org/W4311349482"],"abstract_inverted_index":{"We":[0,29,39,50],"introduce":[1,10,52],"some":[2,35,42],"new":[3],"classes":[4],"of":[5,36,45],"parameterized":[6,24],"operators.":[7],"First,":[8],"we":[9,14,57],"an":[11,53],"operator":[12,32,55],"that":[13,56],"call":[15,58],"the":[16,59],"reduced":[17,47],"t-norm,":[18],"which":[19,62],"is":[20,63],"obtained":[21,64],"by":[22,65],"a":[23,27,67,70],"deviation":[25],"from":[26],"t-norm.":[28],"study":[30],"this":[31,46],"and":[33],"develop":[34],"its":[37],"properties.":[38],"also":[40],"investigate":[41],"special":[43],"cases":[44],"t-norm":[48],"operator.":[49],"then":[51],"analogous":[54],"augmented":[60],"t-conorm":[61],"adding":[66],"value":[68],"to":[69],"t-conorm.":[71]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
