{"id":"https://openalex.org/W4401337546","doi":"https://doi.org/10.1109/fuzz-ieee60900.2024.10611928","title":"Grouping Indices: Definition, Properties and Construction Methods","display_name":"Grouping Indices: Definition, Properties and Construction Methods","publication_year":2024,"publication_date":"2024-06-30","ids":{"openalex":"https://openalex.org/W4401337546","doi":"https://doi.org/10.1109/fuzz-ieee60900.2024.10611928"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee60900.2024.10611928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee60900.2024.10611928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","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/A5053196020","display_name":"Gra\u00e7aliz Pereira Dimuro","orcid":"https://orcid.org/0000-0001-6986-9888"},"institutions":[{"id":"https://openalex.org/I126460647","display_name":"Universidade Federal do Rio Grande","ror":"https://ror.org/05hpfkn88","country_code":"BR","type":"education","lineage":["https://openalex.org/I126460647"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Gra\u00e7aliz Pereira Dimuro","raw_affiliation_strings":["Centro de Ci&#x00EA;ncias Computacionais, Universidade Federal do Rio Grande,Rio Grande,Brazil"],"affiliations":[{"raw_affiliation_string":"Centro de Ci&#x00EA;ncias Computacionais, Universidade Federal do Rio Grande,Rio Grande,Brazil","institution_ids":["https://openalex.org/I126460647"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033482780","display_name":"H\u00e9lida Santos","orcid":"https://orcid.org/0000-0003-2994-2862"},"institutions":[{"id":"https://openalex.org/I126460647","display_name":"Universidade Federal do Rio Grande","ror":"https://ror.org/05hpfkn88","country_code":"BR","type":"education","lineage":["https://openalex.org/I126460647"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Helida Salles Santos","raw_affiliation_strings":["Centro de Ci&#x00EA;ncias Computacionais, Universidade Federal do Rio Grande,Rio Grande,Brazil"],"affiliations":[{"raw_affiliation_string":"Centro de Ci&#x00EA;ncias Computacionais, Universidade Federal do Rio Grande,Rio Grande,Brazil","institution_ids":["https://openalex.org/I126460647"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099516423","display_name":"Asier Urio-Larrea","orcid":"https://orcid.org/0000-0001-7667-5766"},"institutions":[{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Asier Urio-Larrea","raw_affiliation_strings":["Inform&#x00E1; tica y Matem&#x00E1;ticas, Universidad P&#x00FA; blica de Navarra,Depto. Estad.,Pamplona,Spain"],"affiliations":[{"raw_affiliation_string":"Inform&#x00E1; tica y Matem&#x00E1;ticas, Universidad P&#x00FA; blica de Navarra,Depto. Estad.,Pamplona,Spain","institution_ids":["https://openalex.org/I88155538"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037049485","display_name":"Tiago da Cruz Asmus","orcid":"https://orcid.org/0000-0002-7066-7156"},"institutions":[{"id":"https://openalex.org/I126460647","display_name":"Universidade Federal do Rio Grande","ror":"https://ror.org/05hpfkn88","country_code":"BR","type":"education","lineage":["https://openalex.org/I126460647"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Tiago Asmus","raw_affiliation_strings":["Inst. Matem&#x00E1;tica, Estat&#x00ED; stica e F&#x00ED;sica, Universidade Federal do Rio Grande,Rio Grande,Brazil"],"affiliations":[{"raw_affiliation_string":"Inst. Matem&#x00E1;tica, Estat&#x00ED; stica e F&#x00ED;sica, Universidade Federal do Rio Grande,Rio Grande,Brazil","institution_ids":["https://openalex.org/I126460647"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031787326","display_name":"Giancarlo Lucca","orcid":"https://orcid.org/0000-0002-3776-0260"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giancarlo Lucca","raw_affiliation_strings":["PPG em Eng. Eletr&#x00F4;nica e Computa&#x00E7;&#x00E3;o, Universidade Cat&#x00F3;lica de Pelotas,Pelotas,Brazil"],"affiliations":[{"raw_affiliation_string":"PPG em Eng. Eletr&#x00F4;nica e Computa&#x00E7;&#x00E3;o, Universidade Cat&#x00F3;lica de Pelotas,Pelotas,Brazil","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037198516","display_name":"Heloisa A. Camargo","orcid":"https://orcid.org/0000-0002-5489-7306"},"institutions":[{"id":"https://openalex.org/I177909021","display_name":"Universidade Federal de S\u00e3o Carlos","ror":"https://ror.org/00qdc6m37","country_code":"BR","type":"education","lineage":["https://openalex.org/I177909021"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Heloisa Camargo","raw_affiliation_strings":["Universidade Federal de S&#x00E3;o Carlos,Departamento de Computa&#x00E7;&#x00E3;o,S&#x00E3;o Carlos,Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade Federal de S&#x00E3;o Carlos,Departamento de Computa&#x00E7;&#x00E3;o,S&#x00E3;o Carlos,Brazil","institution_ids":["https://openalex.org/I177909021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106284366","display_name":"Maria Eug\u00eania Parodi","orcid":null},"institutions":[{"id":"https://openalex.org/I126460647","display_name":"Universidade Federal do Rio Grande","ror":"https://ror.org/05hpfkn88","country_code":"BR","type":"education","lineage":["https://openalex.org/I126460647"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Maria Eug\u00eania Parodi","raw_affiliation_strings":["Programa de P&#x00F3; s-Gradua&#x00E7;&#x00E3;o em Modelagem Computacional, Universidade Federal do Rio Grande,Rio Grande,Brazil"],"affiliations":[{"raw_affiliation_string":"Programa de P&#x00F3; s-Gradua&#x00E7;&#x00E3;o em Modelagem Computacional, Universidade Federal do Rio Grande,Rio Grande,Brazil","institution_ids":["https://openalex.org/I126460647"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049375194","display_name":"Humberto Bustince","orcid":"https://orcid.org/0000-0002-1279-6195"},"institutions":[{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Humberto Bustince","raw_affiliation_strings":["Inform&#x00E1;tica y Matem&#x00E1;ticas, Universidad P&#x00FA;blica de Navarra,Departamento de Estad&#x00ED;stica,Pamplona,Spain"],"affiliations":[{"raw_affiliation_string":"Inform&#x00E1;tica y Matem&#x00E1;ticas, Universidad P&#x00FA;blica de Navarra,Departamento de Estad&#x00ED;stica,Pamplona,Spain","institution_ids":["https://openalex.org/I88155538"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5053196020"],"corresponding_institution_ids":["https://openalex.org/I126460647"],"apc_list":null,"apc_paid":null,"fwci":0.4801,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6740361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9987999796867371,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9987999796867371,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9843000173568726,"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":0.972100019454956,"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/computer-science","display_name":"Computer science","score":0.6017754673957825}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6017754673957825}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/fuzz-ieee60900.2024.10611928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee60900.2024.10611928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"},{"id":"pmh:oai:academica-e.unavarra.es:2454/55338","is_oa":false,"landing_page_url":"https://hdl.handle.net/2454/55338","pdf_url":null,"source":{"id":"https://openalex.org/S4306402560","display_name":"Academica-e (Universidad P\u00fablica de Navarra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I175051016","host_organization_name":"Universidad Publica de Navarra","host_organization_lineage":["https://openalex.org/I175051016"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/acceptedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1312179244","display_name":null,"funder_award_id":"304118/2023-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G1589553732","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3030070273","display_name":null,"funder_award_id":"407206/2023-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3429648993","display_name":null,"funder_award_id":"PID202","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4816244515","display_name":null,"funder_award_id":"FEDER","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5079005330","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G586857820","display_name":null,"funder_award_id":"501100011033/FEDER","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6071709581","display_name":null,"funder_award_id":"13039/501100011033/","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320324610","display_name":"Universidad P\u00fablica de Navarra","ror":"https://ror.org/02z0cah89"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1545067530","https://openalex.org/W1821293446","https://openalex.org/W1983659965","https://openalex.org/W1998690720","https://openalex.org/W2008553971","https://openalex.org/W2073824442","https://openalex.org/W2222312669","https://openalex.org/W2282429601","https://openalex.org/W2296349740","https://openalex.org/W2322552805","https://openalex.org/W2503986321","https://openalex.org/W2523416820","https://openalex.org/W2549922524","https://openalex.org/W2621268638","https://openalex.org/W2797955680","https://openalex.org/W2885083530","https://openalex.org/W2976260192","https://openalex.org/W3014408868","https://openalex.org/W3135013915","https://openalex.org/W3156271459","https://openalex.org/W3158266344","https://openalex.org/W3199835548","https://openalex.org/W3202288348","https://openalex.org/W4200455479","https://openalex.org/W4211007335","https://openalex.org/W4230588984","https://openalex.org/W4242872809","https://openalex.org/W4285200946","https://openalex.org/W4285225895","https://openalex.org/W4285507643","https://openalex.org/W4295767965","https://openalex.org/W4300862412","https://openalex.org/W4309632766","https://openalex.org/W4311256623","https://openalex.org/W4361295360","https://openalex.org/W4381486722","https://openalex.org/W4387394891","https://openalex.org/W4387546683","https://openalex.org/W4388678048","https://openalex.org/W4389118005","https://openalex.org/W6725194071"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Zadeh":[0],"has":[1],"defined":[2],"its":[3,68],"consistency":[4],"index":[5,91],"<tex":[6,16,20,27,36,45,92,99,103,118,122,129,136,144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,17,21,28,37,46,93,100,104,119,123,130,137,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$O_{Z}$</tex>":[8],"in":[9,30,59,62,70,74,81],"order":[10],"to":[11,44,125,143],"compare":[12],"two":[13,96],"fuzzy":[14,97,115],"subsets":[15,98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$A$</tex>":[18,101,120],"and":[19,76,102,121,155,167],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$B$</tex>":[22,105,124],"of":[23,53,64,95,110,113,117],"a":[24,89,108],"referential":[25,127],"set":[26,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$U$</tex>,":[29,131],"the":[31,42,60,86,111,114,126,141,162],"sense":[32],"that":[33,106,132],"\u201cThe":[34],"lower":[35],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$O_{Z}":[38],"(A,":[39],"B)$</tex>":[40,139],"is,":[41,133,140],"closer":[43,142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\emptyset":[47],"A\\cap":[48],"B$</tex>":[49,148],"is.\u201d":[50,149],"Several":[51],"axiomatizations":[52],"this":[54],"concept":[55],"can":[56],"be":[57],"found":[58],"literature,":[61],"terms":[63],"overlap":[65,166],"indices,":[66],"allowing":[67],"application":[69],"different":[71],"contexts,":[72],"as":[73],"classification":[75],"clustering.":[77],"The":[78,172],"present":[79],"work,":[80],"an":[82],"opposite":[83],"direction,":[84],"introduces":[85],"grouping":[87,168],"index,":[88],"comparison":[90],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathcal{G}$</tex>":[94],"provides":[107],"measure":[109],"proximity":[112],"union":[116],"'the":[134],"higher":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mathcal{G}(A,":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$U":[146],"A\\cup":[147],"Many":[150],"important":[151],"properties":[152],"are":[153,158],"analyzed,":[154],"construction":[156],"methods":[157],"presented,":[159],"whereas":[160],"establishing":[161],"formal":[163],"relation":[164],"between":[165],"indices":[169],"via":[170],"duality.":[171],"theory":[173],"is":[174],"illustrated":[175],"by":[176],"several":[177],"detailed":[178],"examples.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
