{"id":"https://openalex.org/W4316660664","doi":"https://doi.org/10.1109/tfuzz.2023.3235405","title":"From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets","display_name":"From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets","publication_year":2023,"publication_date":"2023-01-16","ids":{"openalex":"https://openalex.org/W4316660664","doi":"https://doi.org/10.1109/tfuzz.2023.3235405"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2023.3235405","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tfuzz.2023.3235405","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/A5014677775","display_name":"Mikel Ferrero-Jaurrieta","orcid":"https://orcid.org/0000-0002-6854-3437"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]},{"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":"Mikel Ferrero-Jaurrieta","raw_affiliation_strings":["Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6854-3437","affiliations":[{"raw_affiliation_string":"Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016","https://openalex.org/I88155538"]}]},{"author_position":"middle","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 Tak\u00e1\u010d","raw_affiliation_strings":["Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia"],"raw_orcid":"https://orcid.org/0000-0003-0767-4756","affiliations":[{"raw_affiliation_string":"Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia","institution_ids":["https://openalex.org/I110757952"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041159639","display_name":"Iosu Rodr\u00edguez-Mart\u00ednez","orcid":"https://orcid.org/0000-0002-9960-0203"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]},{"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":"Iosu Rodriguez-Martinez","raw_affiliation_strings":["Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016","https://openalex.org/I88155538"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006086361","display_name":"C\u00e9dric Marco-Detchart","orcid":"https://orcid.org/0000-0002-4310-9060"},"institutions":[{"id":"https://openalex.org/I4210131846","display_name":"Artificial Intelligence Research Institute","ror":"https://ror.org/03c0ach84","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210131846"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Cedric Marco-Detchart","raw_affiliation_strings":["Valencian Research Institute for Artificial Intelligence (VRAIN), Universitat Polit&#x00E8;cnica de Val&#x00E8;ncia, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Valencian Research Institute for Artificial Intelligence (VRAIN), Universitat Polit&#x00E8;cnica de Val&#x00E8;ncia, Valencia, Spain","institution_ids":["https://openalex.org/I4210131846"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046403060","display_name":"Angela Bernardini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angela Bernardini","raw_affiliation_strings":["NAITEC, Technological Center for Automotive and Mechatronics, Pamplona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NAITEC, Technological Center for Automotive and Mechatronics, Pamplona, Spain","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085226753","display_name":"Javier Fern\u00e1ndez","orcid":"https://orcid.org/0000-0003-4427-3935"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]},{"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":"Javier Fern\u00e1ndez","raw_affiliation_strings":["Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4427-3935","affiliations":[{"raw_affiliation_string":"Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016","https://openalex.org/I88155538"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056125713","display_name":"Carlos L\u00f3pez-Molina","orcid":"https://orcid.org/0000-0002-0904-9834"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]},{"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":"Carlos Lopez-Molina","raw_affiliation_strings":["Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0904-9834","affiliations":[{"raw_affiliation_string":"Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016","https://openalex.org/I88155538"]}]},{"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/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]},{"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":["Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-1279-6195","affiliations":[{"raw_affiliation_string":"Departament of Statistics, Computer Science and Mathematics, Public University of Navarra, Pamplona, Spain","institution_ids":["https://openalex.org/I175051016","https://openalex.org/I88155538"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8534,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72021858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"31","issue":"8","first_page":"2709","last_page":"2721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9882000088691711,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9882000088691711,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9769999980926514,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9765999913215637,"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/notation","display_name":"Notation","score":0.686920166015625},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6357426643371582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5921328067779541},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.4487074613571167},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.42940157651901245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4093891382217407},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3507043123245239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2664165496826172},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25139671564102173},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1712242066860199},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13391846418380737},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12458354234695435}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.686920166015625},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6357426643371582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5921328067779541},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4487074613571167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.42940157651901245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4093891382217407},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3507043123245239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2664165496826172},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25139671564102173},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1712242066860199},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13391846418380737},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12458354234695435},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tfuzz.2023.3235405","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tfuzz.2023.3235405","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"},{"id":"pmh:oai:academica-e.unavarra.es:2454/45222","is_oa":false,"landing_page_url":"https://hdl.handle.net/2454/45222","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 P\u00fablica de Navarra (UPNA)","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/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W151607323","https://openalex.org/W184846395","https://openalex.org/W1480546554","https://openalex.org/W1480794475","https://openalex.org/W1606108510","https://openalex.org/W1892813713","https://openalex.org/W1905771608","https://openalex.org/W1970986794","https://openalex.org/W1976443301","https://openalex.org/W1992490931","https://openalex.org/W1998085025","https://openalex.org/W2005076113","https://openalex.org/W2008230680","https://openalex.org/W2020141350","https://openalex.org/W2022270025","https://openalex.org/W2022735534","https://openalex.org/W2033810643","https://openalex.org/W2036430002","https://openalex.org/W2037955148","https://openalex.org/W2041798388","https://openalex.org/W2048288497","https://openalex.org/W2049059095","https://openalex.org/W2049442812","https://openalex.org/W2056021265","https://openalex.org/W2056591797","https://openalex.org/W2063972032","https://openalex.org/W2067191022","https://openalex.org/W2068233430","https://openalex.org/W2079809266","https://openalex.org/W2087424102","https://openalex.org/W2099244020","https://openalex.org/W2107180976","https://openalex.org/W2130902850","https://openalex.org/W2150134853","https://openalex.org/W2227159142","https://openalex.org/W2264784471","https://openalex.org/W2296349740","https://openalex.org/W2332753032","https://openalex.org/W2346329485","https://openalex.org/W2602556226","https://openalex.org/W2613399694","https://openalex.org/W4233165551","https://openalex.org/W4252793191","https://openalex.org/W4253974119","https://openalex.org/W4307334310","https://openalex.org/W6607458260","https://openalex.org/W6628742311","https://openalex.org/W6802386830"],"related_works":["https://openalex.org/W2018206907","https://openalex.org/W1034061887","https://openalex.org/W4248699163","https://openalex.org/W2027762620","https://openalex.org/W1969792448","https://openalex.org/W2623511688","https://openalex.org/W2786979983","https://openalex.org/W4236314829","https://openalex.org/W2004624959","https://openalex.org/W1986866994"],"abstract_inverted_index":{"Restricted":[0],"equivalence":[1,26,63,78],"functions":[2,5,27,42,79],"are":[3],"well-known":[4],"to":[6,43,60,67,85],"compare":[7,68],"two":[8],"numbers":[9],"in":[10,104],"the":[11,18,22,50,61,74,105],"interval":[12],"between":[13],"0":[14],"and":[15,28,90],"1.":[16],"Despite":[17],"numerous":[19],"works":[20],"studying":[21],"properties":[23],"of":[24,40,76,107,115,117],"restricted":[25,62,77],"their":[29],"multiple":[30],"applications":[31],"as":[32,112],"support":[33],"for":[34],"different":[35],"similarity":[36,94],"measures,":[37],"an":[38,44,113],"extension":[39],"these":[41],"n-dimensional":[45],"space":[46],"is":[47,102],"absent":[48],"from":[49,80],"literature.":[51],"In":[52],"this":[53],"article,":[54],"we":[55,72],"present":[56,91],"a":[57,92],"novel":[58],"contribution":[59],"function":[64],"theory,":[65],"allowing":[66],"multivalued":[69],"elements.":[70],"Specifically,":[71],"extend":[73],"notion":[75],"<inline-formula":[81,86,97],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[82,87,98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[83,88,99],"notation=\"LaTeX\">$L$</tex-math></inline-formula>":[84],"notation=\"LaTeX\">$L^{n}$</tex-math></inline-formula>":[89],"new":[93],"construction":[95],"on":[96],"notation=\"LaTeX\">$L^{n}$</tex-math></inline-formula>.":[100],"proposal":[101],"tested":[103],"context":[106],"color":[108],"image":[109],"anisotropic":[110],"diffusion":[111],"example":[114],"one":[116],"its":[118],"many":[119],"applications.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}