{"id":"https://openalex.org/W4401507678","doi":"https://doi.org/10.1109/access.2024.3441940","title":"On Gradual Sets, Hesitant Fuzzy Sets, and Representation Theorems","display_name":"On Gradual Sets, Hesitant Fuzzy Sets, and Representation Theorems","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4401507678","doi":"https://doi.org/10.1109/access.2024.3441940"},"language":"en","primary_location":{"id":"doi:10.1109/access.2024.3441940","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3441940","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dx.doi.org/10.1109/access.2024.3441940","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021368317","display_name":"Pascual Jara","orcid":"https://orcid.org/0000-0003-0367-3465"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Pascual Jara","raw_affiliation_strings":["Department of Algebra, University of Granada, Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, University of Granada, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060547894","display_name":"Luis Merino","orcid":"https://orcid.org/0000-0002-3531-3184"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Luis Merino","raw_affiliation_strings":["Department of Algebra, University of Granada, Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, University of Granada, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102008815","display_name":"Gabriel Navarro","orcid":"https://orcid.org/0000-0002-9895-5686"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gabriel Navarro","raw_affiliation_strings":["Department of Algebra, University of Granada, Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, University of Granada, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047039674","display_name":"Evangelina Santos","orcid":"https://orcid.org/0000-0001-8842-0824"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Evangelina Santos","raw_affiliation_strings":["Department of Algebra, University of Granada, Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, University of Granada, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021368317"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15524404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":null,"first_page":"111158","last_page":"111168"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9984999895095825,"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":0.9984999895095825,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9977999925613403,"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":0.996999979019165,"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/computer-science","display_name":"Computer science","score":0.6108564138412476},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5644780993461609},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5625611543655396},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.45213523507118225},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4248102009296417},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3626444339752197},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32591181993484497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3234679698944092},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2658652067184448}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6108564138412476},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5644780993461609},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5625611543655396},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.45213523507118225},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4248102009296417},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3626444339752197},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32591181993484497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3234679698944092},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2658652067184448},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/access.2024.3441940","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3441940","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:digibug.ugr.es:10481/93846","is_oa":true,"landing_page_url":"https://hdl.handle.net/10481/93846","pdf_url":"https://digibug.ugr.es/bitstream/10481/93846/1/On_Gradual_Sets_Hesitant_Fuzzy_Sets_and_Representation_Theorems.pdf","source":{"id":"https://openalex.org/S4306400567","display_name":"Institutional Repository of the University of Granada (University of Granada)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173304897","host_organization_name":"Universidad de Granada","host_organization_lineage":["https://openalex.org/I173304897"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},{"id":"pmh:oai:doaj.org/article:4ad63f64f6ff420199bfc165cbcac8aa","is_oa":true,"landing_page_url":"https://doaj.org/article/4ad63f64f6ff420199bfc165cbcac8aa","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 12, Pp 111158-111168 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2024.3441940","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3441940","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1320060331","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/50110001103","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1368337324","display_name":null,"funder_award_id":"CEX2020-001105-M","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1598597440","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/5011000110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G21826877","display_name":null,"funder_award_id":"CEX2020-001105-M","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"},{"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/G2969783435","display_name":null,"funder_award_id":"CIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3219925899","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","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/G3918395066","display_name":null,"funder_award_id":"FQM-394","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"},{"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/G4456466100","display_name":null,"funder_award_id":"2020-001105","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4668258890","display_name":null,"funder_award_id":"UGR20","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"},{"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/G5080475149","display_name":null,"funder_award_id":"10.13039","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/G7535663061","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/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8638682022","display_name":null,"funder_award_id":"10.13039/50110001103","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8716935391","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"}],"funders":[{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"},{"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":18,"referenced_works":["https://openalex.org/W1975212232","https://openalex.org/W1979071538","https://openalex.org/W1980564456","https://openalex.org/W2009874049","https://openalex.org/W2038270820","https://openalex.org/W2051734340","https://openalex.org/W2054416947","https://openalex.org/W2057821010","https://openalex.org/W2120713972","https://openalex.org/W2164214149","https://openalex.org/W2282429601","https://openalex.org/W2385027037","https://openalex.org/W2767961414","https://openalex.org/W2991144196","https://openalex.org/W4239165868","https://openalex.org/W4245152641","https://openalex.org/W4312408255","https://openalex.org/W4322489540"],"related_works":["https://openalex.org/W2062195135","https://openalex.org/W2795079307","https://openalex.org/W2793058541","https://openalex.org/W2155782347","https://openalex.org/W2117174108","https://openalex.org/W3097058627","https://openalex.org/W4230722584","https://openalex.org/W3146062725","https://openalex.org/W2215186495","https://openalex.org/W2127878690"],"abstract_inverted_index":{"We":[0,44,103],"analyze":[1],"the":[2,11,16,29,71,105,119,129],"connection":[3],"between":[4,40],"two":[5,42],"perspectives":[6],"when":[7,95],"defining":[8],"fuzzy":[9,48,93,110,122,133,137,146,163,173],"sets:":[10],"viewpoint":[12,17],"of":[13,18,20,31,100,121,132,145,150,161],"mappings":[14],"and":[15,50,62,73,115],"families":[19,99],"level":[21,101],"cuts.":[22,102],"This":[23,59],"analysis":[24],"is":[25,175],"mathematically":[26],"supported":[27],"by":[28],"framework":[30],"a":[32,38,166,168],"categorical":[33],"adjunction,":[34],"which":[35],"serves":[36],"as":[37,77,98,124,135,148],"dictionary":[39],"these":[41],"perspectives.":[43],"prove":[45],"that":[46,118],"hesitant":[47,136],"sets":[49,52,111,123,126,134,147,174],"gradual":[51,85,125],"are":[53],"strongly":[54],"related":[55],"through":[56],"this":[57,113,155],"connection.":[58],"allows":[60],"concepts":[61],"operations":[63,83,91],"to":[64,70,157],"be":[65],"transferred":[66],"from":[67],"one":[68],"class":[69],"other,":[72],"vice":[74],"versa.":[75],"Concretely,":[76],"an":[78],"application,":[79],"we":[80,116,153],"provide":[81],"lattice":[82],"on":[84,92,128],"sets,":[86,94],"compatible":[87],"with":[88],"Zadeh\u2019s":[89],"max-min":[90],"considering":[96],"them":[97],"discuss":[104],"well-known":[106],"representation":[107,120,169],"theorem":[108,170],"for":[109,171],"within":[112],"framework,":[114],"show":[117],"depends":[127],"chosen":[130],"embedding":[131],"sets.":[138,164],"Hence,":[139],"distinct":[140],"embeddings":[141],"yield":[142],"diverse":[143],"representations":[144],"collections":[149],"subsets.":[151],"Furthermore,":[152],"extend":[154],"methodology":[156],"include":[158],"other":[159],"classes":[160],"extended":[162],"As":[165],"consequence,":[167],"interval-valued":[172],"provided.":[176]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2024-08-13T00:00:00"}