{"id":"https://openalex.org/W2602038294","doi":"https://doi.org/10.1109/tfuzz.2017.2686372","title":"Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory","display_name":"Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory","publication_year":2017,"publication_date":"2017-03-23","ids":{"openalex":"https://openalex.org/W2602038294","doi":"https://doi.org/10.1109/tfuzz.2017.2686372","mag":"2602038294"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2017.2686372","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2017.2686372","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Fuzzy 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/A5041682469","display_name":"Maria Jos\u00e9 Asi\u00e1in","orcid":"https://orcid.org/0000-0002-6123-1684"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad Publica de Navarra","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Maria J. Asiain","raw_affiliation_strings":["Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain","[Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain]"],"affiliations":[{"raw_affiliation_string":"Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016"]},{"raw_affiliation_string":"[Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain]","institution_ids":["https://openalex.org/I175051016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049375194","display_name":"Humberto Bustince","orcid":"https://orcid.org/0000-0002-1279-6195"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad Publica de Navarra","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Humberto Bustince","raw_affiliation_strings":["Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain","[Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain]"],"affiliations":[{"raw_affiliation_string":"Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016"]},{"raw_affiliation_string":"[Departamentos de Matem\u00e1ticas y Autom\u00e1tica y Computaci\u00f3n, Universidad P\u00fablica de Navarra, Pamplona, Spain]","institution_ids":["https://openalex.org/I175051016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058341815","display_name":"Radko Mesiar","orcid":"https://orcid.org/0000-0001-6503-949X"},"institutions":[{"id":"https://openalex.org/I187293425","display_name":"University of Ostrava","ror":"https://ror.org/00pyqav47","country_code":"CZ","type":"education","lineage":["https://openalex.org/I187293425"]},{"id":"https://openalex.org/I110757952","display_name":"Slovak University of Technology in Bratislava","ror":"https://ror.org/0561ghm58","country_code":"SK","type":"education","lineage":["https://openalex.org/I110757952"]}],"countries":["CZ","SK"],"is_corresponding":false,"raw_author_name":"Radko Mesiar","raw_affiliation_strings":["Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia","Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia","institution_ids":["https://openalex.org/I110757952"]},{"raw_affiliation_string":"Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic","institution_ids":["https://openalex.org/I187293425"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024224758","display_name":"Anna Koles\u00e1rov\u00e1","orcid":"https://orcid.org/0000-0001-6438-0039"},"institutions":[{"id":"https://openalex.org/I110757952","display_name":"Slovak University of Technology in Bratislava","ror":"https://ror.org/0561ghm58","country_code":"SK","type":"education","lineage":["https://openalex.org/I110757952"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Anna Kolesarova","raw_affiliation_strings":["Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovak"],"affiliations":[{"raw_affiliation_string":"Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovak","institution_ids":["https://openalex.org/I110757952"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007012513","display_name":"Zdenko Tak\u00e1\u010d","orcid":"https://orcid.org/0000-0003-0767-4756"},"institutions":[{"id":"https://openalex.org/I110757952","display_name":"Slovak University of Technology in Bratislava","ror":"https://ror.org/0561ghm58","country_code":"SK","type":"education","lineage":["https://openalex.org/I110757952"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Zdenko Takac","raw_affiliation_strings":["Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovak"],"affiliations":[{"raw_affiliation_string":"Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovak","institution_ids":["https://openalex.org/I110757952"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5041682469"],"corresponding_institution_ids":["https://openalex.org/I175051016"],"apc_list":null,"apc_paid":null,"fwci":6.9748,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.96920411,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"26","issue":"2","first_page":"556","last_page":"568"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and 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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.8038902878761292},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.6415817737579346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.630279004573822},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.6218313574790955},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5541293025016785},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5506713390350342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4838920533657074},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.44776472449302673},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43703004717826843},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4364608824253082},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31844189763069153},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28779420256614685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2835232615470886},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2653774619102478}],"concepts":[{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.8038902878761292},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.6415817737579346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.630279004573822},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.6218313574790955},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5541293025016785},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5506713390350342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4838920533657074},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.44776472449302673},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43703004717826843},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4364608824253082},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31844189763069153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28779420256614685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2835232615470886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2653774619102478},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2017.2686372","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2017.2686372","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3697008090","display_name":null,"funder_award_id":"1/0420/15","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"}],"funders":[{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W40618249","https://openalex.org/W112993705","https://openalex.org/W230325874","https://openalex.org/W656973277","https://openalex.org/W1600819735","https://openalex.org/W1654095111","https://openalex.org/W1673969116","https://openalex.org/W1788095458","https://openalex.org/W1967885240","https://openalex.org/W1975503090","https://openalex.org/W1978334434","https://openalex.org/W1981107087","https://openalex.org/W1984974630","https://openalex.org/W1986391289","https://openalex.org/W1988053196","https://openalex.org/W2007805591","https://openalex.org/W2014079765","https://openalex.org/W2017828163","https://openalex.org/W2030330616","https://openalex.org/W2033667126","https://openalex.org/W2036430002","https://openalex.org/W2054976600","https://openalex.org/W2060907774","https://openalex.org/W2068233430","https://openalex.org/W2068402605","https://openalex.org/W2074537354","https://openalex.org/W2078443809","https://openalex.org/W2087424102","https://openalex.org/W2105429025","https://openalex.org/W2107217767","https://openalex.org/W2120549556","https://openalex.org/W2123964448","https://openalex.org/W2131429285","https://openalex.org/W2132685025","https://openalex.org/W2133059825","https://openalex.org/W2144832785","https://openalex.org/W2148925928","https://openalex.org/W2282429601","https://openalex.org/W2423020222","https://openalex.org/W2503986321","https://openalex.org/W4233658823","https://openalex.org/W6725194071"],"related_works":["https://openalex.org/W1985455246","https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W2059922809","https://openalex.org/W2803221307","https://openalex.org/W2951826204","https://openalex.org/W4211001408","https://openalex.org/W2366147410","https://openalex.org/W62366039"],"abstract_inverted_index":{"Admissible":[0],"orders":[1,26,95],"have":[2,116],"brought":[3],"the":[4,9,31,38,55,81,106],"structure":[5],"of":[6,11,19,40,83,101],"chains":[7],"in":[8,30,52],"framework":[10],"interval-valued":[12],"fuzzy":[13,124],"sets.":[14],"However,":[15],"a":[16,117],"deeper":[17],"study":[18],"functions":[20],"monotone":[21],"with":[22,47,88,127],"respect":[23,48,89],"to":[24,49,80,90,130],"admissible":[25,50],"is":[27],"still":[28],"missing":[29],"literature.":[32],"In":[33],"this":[34],"work,":[35],"we":[36],"consider":[37],"construction":[39,82],"negations":[41,44,85,103,115],"and":[42,57,59,76],"strong":[43,84,102,114],"on":[45,68,86,97,120],"intervals":[46,87],"orders,":[51,61],"particular,":[53],"for":[54,65],"Xu":[56],"Yager":[58],"lexicographical":[60],"as":[62,64],"well":[63],"those":[66],"based":[67,96],"K":[69,91],"<sub":[70,92],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[71,93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sub>":[72],"operators.":[73],"We":[74],"introduce":[75,131],"discuss":[77],"an":[78,98],"approach":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1,\u03b2</sub>":[94],"arbitrary":[99],"couple":[100],"defined":[104],"over":[105],"standard":[107],"real":[108],"interval":[109],"[0,":[110],"1].":[111],"The":[112],"introduced":[113],"deep":[118],"impact":[119],"all":[121],"fields":[122],"exploiting":[123],"methods":[125],"dealing":[126],"intervals,":[128],"allowing":[129],"complements,":[132],"dual":[133],"aggregations,":[134],"implications,":[135],"entropies,":[136],"etc.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
