{"id":"https://openalex.org/W4293415445","doi":"https://doi.org/10.3390/axioms11090431","title":"Relaxed Indistinguishability Relations and Relaxed Metrics: The Aggregation Problem","display_name":"Relaxed Indistinguishability Relations and Relaxed Metrics: The Aggregation Problem","publication_year":2022,"publication_date":"2022-08-26","ids":{"openalex":"https://openalex.org/W4293415445","doi":"https://doi.org/10.3390/axioms11090431"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11090431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090431","pdf_url":"https://www.mdpi.com/2075-1680/11/9/431/pdf?version=1663840363","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/9/431/pdf?version=1663840363","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063129002","display_name":"Juan-De-Dios Gonz\u00e1lez-Hedstr\u00f6m","orcid":null},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan-De-Dios Gonz\u00e1lez-Hedstr\u00f6m","raw_affiliation_strings":["Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051641741","display_name":"Juan-Jos\u00e9 Mi\u00f1ana","orcid":"https://orcid.org/0000-0001-9835-0700"},"institutions":[{"id":"https://openalex.org/I4210126021","display_name":"Health Research Institute of the Balearic Islands","ror":"https://ror.org/037xbgq12","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210126021"]},{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan-Jos\u00e9 Mi\u00f1ana","raw_affiliation_strings":["Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain","Institut d\u2019 Investigaci\u00f3 Sanit\u00e0ria Illes Balears (IdISBa), Hospital Universitari Son Espases, 07120 Palma de Mallorca, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]},{"raw_affiliation_string":"Institut d\u2019 Investigaci\u00f3 Sanit\u00e0ria Illes Balears (IdISBa), Hospital Universitari Son Espases, 07120 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I4210126021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007428198","display_name":"\u00d3scar Valero","orcid":"https://orcid.org/0000-0003-4710-1338"},"institutions":[{"id":"https://openalex.org/I4210126021","display_name":"Health Research Institute of the Balearic Islands","ror":"https://ror.org/037xbgq12","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210126021"]},{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Oscar Valero","raw_affiliation_strings":["Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain","Institut d\u2019 Investigaci\u00f3 Sanit\u00e0ria Illes Balears (IdISBa), Hospital Universitari Son Espases, 07120 Palma de Mallorca, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]},{"raw_affiliation_string":"Institut d\u2019 Investigaci\u00f3 Sanit\u00e0ria Illes Balears (IdISBa), Hospital Universitari Son Espases, 07120 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I4210126021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051641741"],"corresponding_institution_ids":["https://openalex.org/I4210126021","https://openalex.org/I50441567"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5085,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68526743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"9","first_page":"431","last_page":"431"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9941999912261963,"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":0.9941999912261963,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9840999841690063,"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/merge","display_name":"Merge (version control)","score":0.7525612115859985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6527275443077087},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5991926789283752},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.5530077219009399},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4311401844024658},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.42556023597717285},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4142058789730072},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3226291537284851},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.31106480956077576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.269977331161499},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12054207921028137}],"concepts":[{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.7525612115859985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6527275443077087},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5991926789283752},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.5530077219009399},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4311401844024658},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.42556023597717285},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4142058789730072},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3226291537284851},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.31106480956077576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.269977331161499},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12054207921028137},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/axioms11090431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090431","pdf_url":"https://www.mdpi.com/2075-1680/11/9/431/pdf?version=1663840363","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:docusalut.com:20.500.13003/18493","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.13003/18493","pdf_url":"https://docusalut.com/bitstream/20.500.13003/18493/1/axioms_2022-11-431.pdf","source":{"id":"https://openalex.org/S4306402504","display_name":"Docusalut (Conselleria de Salut i Consum del Govern de les Illes Balears)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210089844","host_organization_name":"Servei de Salut de les Illes Balears","host_organization_lineage":["https://openalex.org/I4210089844"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:doaj.org/article:7aaeaa7cc1114595924743abd37071bb","is_oa":true,"landing_page_url":"https://doaj.org/article/7aaeaa7cc1114595924743abd37071bb","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":"Axioms, Vol 11, Iss 9, p 431 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/9/431/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11090431","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 9; Pages: 431","raw_type":"Text"},{"id":"pmh:oai:riunet.upv.es:10251/199522","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/199522","pdf_url":null,"source":{"id":"https://openalex.org/S4306401500","display_name":"RiuNet (Politechnical University of Valencia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/axioms11090431","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090431","pdf_url":"https://www.mdpi.com/2075-1680/11/9/431/pdf?version=1663840363","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.7300000190734863,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2245201010","display_name":null,"funder_award_id":"871260","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2568093864","display_name":null,"funder_award_id":"PGC2018-095709-B-C21","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293415445.pdf","grobid_xml":"https://content.openalex.org/works/W4293415445.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W144230659","https://openalex.org/W204971984","https://openalex.org/W410960918","https://openalex.org/W1606108510","https://openalex.org/W1641527384","https://openalex.org/W1668904657","https://openalex.org/W1967433956","https://openalex.org/W1990938907","https://openalex.org/W1994148336","https://openalex.org/W2009579760","https://openalex.org/W2014759141","https://openalex.org/W2046807634","https://openalex.org/W2047237092","https://openalex.org/W2047277075","https://openalex.org/W2054171835","https://openalex.org/W2057103955","https://openalex.org/W2080644966","https://openalex.org/W2095516469","https://openalex.org/W2102034987","https://openalex.org/W2152605301","https://openalex.org/W2187080540","https://openalex.org/W2296349740","https://openalex.org/W2481995907","https://openalex.org/W2576055635","https://openalex.org/W2771615471","https://openalex.org/W2774468310","https://openalex.org/W2889653861","https://openalex.org/W2890957415","https://openalex.org/W2902488476","https://openalex.org/W2981319635","https://openalex.org/W3036178911","https://openalex.org/W3082959223","https://openalex.org/W3123685029","https://openalex.org/W3157733236","https://openalex.org/W3176506620","https://openalex.org/W4233555590","https://openalex.org/W4234672050","https://openalex.org/W4252793191","https://openalex.org/W4300958603","https://openalex.org/W6638465604","https://openalex.org/W6686458478","https://openalex.org/W6741174394"],"related_works":["https://openalex.org/W87675884","https://openalex.org/W154406135","https://openalex.org/W2132859092","https://openalex.org/W2166637398","https://openalex.org/W2384503959","https://openalex.org/W2181335288","https://openalex.org/W2012019755","https://openalex.org/W2374152511","https://openalex.org/W2013143463","https://openalex.org/W2320922716"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,25,53,65],"this":[4,62],"paper":[5],"is":[6,47],"to":[7,22,49],"study":[8],"the":[9,35,50],"relationship":[10],"between":[11,80],"those":[12,28,81,88],"functions":[13,29,60,74,82],"that":[14,30,59,89],"aggregate":[15,90],"relaxed":[16,32,66],"indistinguishability":[17,42,55,67,84],"fuzzy":[18,43,56,68,85],"relations":[19,57,69,86],"with":[20],"respect":[21],"a":[23],"collection":[24],"t-norms":[26],"and":[27,41,87],"merge":[31],"pseudo-metrics,":[33],"extending":[34],"classical":[36],"approach":[37],"explored":[38],"for":[39],"pseudo-metrics":[40],"relations.":[44],"Special":[45],"attention":[46],"paid":[48],"distinguished":[51],"class":[52],"SSI-relaxed":[54],"showing":[58],"merging":[61],"special":[63],"type":[64],"can":[70],"be":[71],"expressed":[72],"through":[73],"aggregating":[75,83],"SSD-relaxed":[76],"pseudo-metrics.":[77],"Outstanding":[78],"differences":[79],"their":[91],"counterpart":[92],"separating":[93],"points":[94],"are":[95],"shown.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}