{"id":"https://openalex.org/W1981684054","doi":"https://doi.org/10.1142/s0218488507004716","title":"REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY","display_name":"REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W1981684054","doi":"https://doi.org/10.1142/s0218488507004716","mag":"1981684054"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488507004716","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488507004716","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based 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/A5012631053","display_name":"Glad Deschrijver","orcid":null},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"GLAD DESCHRIJVER","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B\u20139000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B\u20139000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091486233","display_name":"Chris Cornelis","orcid":"https://orcid.org/0000-0002-6852-4041"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"CHRIS CORNELIS","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B\u20139000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B\u20139000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I32597200"],"apc_list":null,"apc_paid":null,"fwci":3.1098,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.91114095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"03","first_page":"345","last_page":"361"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9987999796867371,"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/fuzzy-set","display_name":"Fuzzy set","score":0.7116824388504028},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.7090785503387451},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.64759361743927},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5770415663719177},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5743005871772766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5706292390823364},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5095167756080627},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48851096630096436},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4636387228965759},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4561670422554016},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.43605583906173706},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.41024234890937805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40649497509002686},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3953635096549988},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35233214497566223},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07144469022750854}],"concepts":[{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.7116824388504028},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.7090785503387451},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.64759361743927},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5770415663719177},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5743005871772766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5706292390823364},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5095167756080627},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48851096630096436},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4636387228965759},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4561670422554016},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.43605583906173706},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.41024234890937805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40649497509002686},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3953635096549988},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35233214497566223},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07144469022750854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218488507004716","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488507004716","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.357.6584","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.357.6584","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cwi.ugent.be/Chris/full/ijufks.pdf","raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:385643","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-385643","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0218-4885","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W27370730","https://openalex.org/W65763650","https://openalex.org/W73677366","https://openalex.org/W1971463464","https://openalex.org/W1980564456","https://openalex.org/W1981153708","https://openalex.org/W2006787659","https://openalex.org/W2007805591","https://openalex.org/W2009123512","https://openalex.org/W2025256895","https://openalex.org/W2031241748","https://openalex.org/W2041835507","https://openalex.org/W2054416947","https://openalex.org/W2057679803","https://openalex.org/W2076808107","https://openalex.org/W2089920338","https://openalex.org/W2104817345","https://openalex.org/W2110182592","https://openalex.org/W2131429285","https://openalex.org/W2912565176","https://openalex.org/W4211007335","https://openalex.org/W4250223147","https://openalex.org/W4292078529"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W1485268022","https://openalex.org/W2674573885","https://openalex.org/W1975005191","https://openalex.org/W2331106272","https://openalex.org/W2253053392","https://openalex.org/W1542808721","https://openalex.org/W4361984403","https://openalex.org/W3176863924","https://openalex.org/W173448675"],"abstract_inverted_index":{"Interval-valued":[0],"fuzzy":[1,10,51,66,72,119,130,144],"set":[2,11,52,120,131,145],"theory":[3,12,121],"is":[4,41],"an":[5,82],"increasingly":[6],"popular":[7,116],"extension":[8],"of":[9,61,129],"where":[13],"traditional":[14],"[0,1]-valued":[15],"membership":[16,28],"degrees":[17],"are":[18],"replaced":[19],"by":[20,68,108,136,158],"intervals":[21],"in":[22,36,95],"[0,1]":[23],"that":[24,92,113],"approximate":[25],"the":[26,96,105,109,138,142],"(unknown)":[27],"degrees.":[29],"To":[30],"construct":[31],"suitable":[32],"graded":[33],"logical":[34],"connectives":[35],"this":[37,55,134],"extended":[38],"setting,":[39],"it":[40],"both":[42],"natural":[43],"and":[44,78,112,166],"appropriate":[45],"to":[46,81,115,124,151],"\"reuse\"":[47],"ingredients":[48],"from":[49],"classical":[50],"theory.":[53,132],"In":[54,133],"paper,":[56],"we":[57,149],"compare":[58],"different":[59],"ways":[60],"representing":[62],"operations":[63,70],"on":[64,71,104],"interval-valued":[65,118,143],"sets":[67],"corresponding":[69],"sets,":[73],"study":[74],"their":[75],"intuitive":[76],"semantics,":[77],"relate":[79],"them":[80],"existing,":[83],"purely":[84],"order-theoretical":[85],"approach.":[86],"Our":[87],"approach":[88],"reveals,":[89],"amongst":[90],"others,":[91],"subtle":[93],"differences":[94],"representation":[97],"method":[98],"can":[99],"have":[100],"a":[101,125,162],"major":[102],"impact":[103],"properties":[106],"satisfied":[107],"generated":[110],"operations,":[111],"contrary":[114],"perception,":[117],"hardly":[122],"corresponds":[123],"mere":[126],"twofold":[127],"application":[128,160],"way,":[135],"making":[137],"mathematical":[139,168],"machinery":[140],"behind":[141],"model":[146],"fully":[147],"transparent,":[148],"aim":[150],"foster":[152],"new":[153],"avenues":[154],"for":[155],"its":[156],"exploitation":[157],"offering":[159],"developers":[161],"much":[163],"more":[164],"powerful":[165],"elaborate":[167],"toolbox":[169],"than":[170],"existed":[171],"before.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}