{"id":"https://openalex.org/W3094460049","doi":"https://doi.org/10.3390/sym12101735","title":"The Fourth Axiom of Similarity Measures","display_name":"The Fourth Axiom of Similarity Measures","publication_year":2020,"publication_date":"2020-10-20","ids":{"openalex":"https://openalex.org/W3094460049","doi":"https://doi.org/10.3390/sym12101735","mag":"3094460049"},"language":"en","primary_location":{"id":"doi:10.3390/sym12101735","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101735","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1735/pdf?version=1603353713","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/10/1735/pdf?version=1603353713","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064396327","display_name":"Chun-Hsiao Chu","orcid":"https://orcid.org/0000-0002-1779-130X"},"institutions":[{"id":"https://openalex.org/I152100410","display_name":"Aletheia University","ror":"https://ror.org/00ke8ye77","country_code":"TW","type":"education","lineage":["https://openalex.org/I152100410"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Chun-Hsiao Chu","raw_affiliation_strings":["Department of Tourism, Aletheia University, New Taipei City 25103, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-1779-130X","affiliations":[{"raw_affiliation_string":"Department of Tourism, Aletheia University, New Taipei City 25103, Taiwan","institution_ids":["https://openalex.org/I152100410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075407180","display_name":"Chih-Ping Yen","orcid":"https://orcid.org/0000-0002-1189-4922"},"institutions":[{"id":"https://openalex.org/I143545923","display_name":"Central Police University","ror":"https://ror.org/03xms6995","country_code":"TW","type":"education","lineage":["https://openalex.org/I143545923"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chih-Ping Yen","raw_affiliation_strings":["Department of Information Management, Central Police University, Taoyuan 33304, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-1189-4922","affiliations":[{"raw_affiliation_string":"Department of Information Management, Central Police University, Taoyuan 33304, Taiwan","institution_ids":["https://openalex.org/I143545923"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078005581","display_name":"Yi-Fong Lin","orcid":"https://orcid.org/0000-0003-3728-1013"},"institutions":[{"id":"https://openalex.org/I195761179","display_name":"Hsing Wu University","ror":"https://ror.org/032hca325","country_code":"TW","type":"education","lineage":["https://openalex.org/I195761179"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yi-Fong Lin","raw_affiliation_strings":["Department of Fashion Industry Management, Hsing Wu University, New Taipei City 25103, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-3728-1013","affiliations":[{"raw_affiliation_string":"Department of Fashion Industry Management, Hsing Wu University, New Taipei City 25103, Taiwan","institution_ids":["https://openalex.org/I195761179"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064396327"],"corresponding_institution_ids":["https://openalex.org/I152100410"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3718,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67215128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"10","first_page":"1735","last_page":"1735"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997000098228455,"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":0.9997000098228455,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9911999702453613,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9860000014305115,"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/similarity","display_name":"Similarity (geometry)","score":0.7851505279541016},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6491738557815552},{"id":"https://openalex.org/keywords/similarity-measure","display_name":"Similarity measure","score":0.601374089717865},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6004695892333984},{"id":"https://openalex.org/keywords/correlation-coefficient","display_name":"Correlation coefficient","score":0.5866613388061523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5827317833900452},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5311760902404785},{"id":"https://openalex.org/keywords/pearson-product-moment-correlation-coefficient","display_name":"Pearson product-moment correlation coefficient","score":0.41217541694641113},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4075945019721985},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.38698717951774597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3651915490627289},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3415747880935669},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3339114189147949},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2834620773792267},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2680923342704773},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.09011968970298767},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07871115207672119}],"concepts":[{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.7851505279541016},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6491738557815552},{"id":"https://openalex.org/C2776517306","wikidata":"https://www.wikidata.org/wiki/Q29017317","display_name":"Similarity measure","level":2,"score":0.601374089717865},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6004695892333984},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.5866613388061523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5827317833900452},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5311760902404785},{"id":"https://openalex.org/C55078378","wikidata":"https://www.wikidata.org/wiki/Q1136628","display_name":"Pearson product-moment correlation coefficient","level":2,"score":0.41217541694641113},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4075945019721985},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.38698717951774597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3651915490627289},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3415747880935669},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3339114189147949},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2834620773792267},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2680923342704773},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.09011968970298767},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07871115207672119},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12101735","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101735","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1735/pdf?version=1603353713","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:93e348a6fbee46e9b869aec33120213b","is_oa":true,"landing_page_url":"https://doaj.org/article/93e348a6fbee46e9b869aec33120213b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 10, p 1735 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/10/1735/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12101735","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12101735","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12101735","pdf_url":"https://www.mdpi.com/2073-8994/12/10/1735/pdf?version=1603353713","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8299999833106995,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3094460049.pdf"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W114678508","https://openalex.org/W1528458083","https://openalex.org/W1968673142","https://openalex.org/W1980564456","https://openalex.org/W1980748255","https://openalex.org/W1982618675","https://openalex.org/W1989450147","https://openalex.org/W2019542647","https://openalex.org/W2031241748","https://openalex.org/W2031844028","https://openalex.org/W2033724079","https://openalex.org/W2039791408","https://openalex.org/W2048524688","https://openalex.org/W2052621174","https://openalex.org/W2064820676","https://openalex.org/W2072597121","https://openalex.org/W2084978862","https://openalex.org/W2124970246","https://openalex.org/W2179870001","https://openalex.org/W2195078114","https://openalex.org/W2259635055","https://openalex.org/W2271763973","https://openalex.org/W2308791864","https://openalex.org/W2475545155","https://openalex.org/W2478776642","https://openalex.org/W2511750421","https://openalex.org/W2525562226","https://openalex.org/W2669156789","https://openalex.org/W2751189891","https://openalex.org/W2754194108","https://openalex.org/W2766931335","https://openalex.org/W2773041763","https://openalex.org/W2791213921","https://openalex.org/W2801549086","https://openalex.org/W2809732338","https://openalex.org/W2811080937","https://openalex.org/W2811282961","https://openalex.org/W2890414467","https://openalex.org/W2895814708","https://openalex.org/W2898057330","https://openalex.org/W2909229155","https://openalex.org/W2912565176","https://openalex.org/W2946824468","https://openalex.org/W2965802055","https://openalex.org/W2971598400","https://openalex.org/W2991931291","https://openalex.org/W3006127909","https://openalex.org/W3014298317","https://openalex.org/W3014990737","https://openalex.org/W3032393056","https://openalex.org/W4211007335","https://openalex.org/W4242485941","https://openalex.org/W4285719527","https://openalex.org/W4292295629","https://openalex.org/W6604705501","https://openalex.org/W6685600698","https://openalex.org/W6687591707","https://openalex.org/W6692610964","https://openalex.org/W6694187189","https://openalex.org/W6721359672","https://openalex.org/W6721653804","https://openalex.org/W6725243936","https://openalex.org/W6727942187","https://openalex.org/W6739633590","https://openalex.org/W6742960986","https://openalex.org/W6744338458","https://openalex.org/W6751701905","https://openalex.org/W6755758476","https://openalex.org/W6758227449","https://openalex.org/W6767236564","https://openalex.org/W6770987500","https://openalex.org/W6775189187","https://openalex.org/W6825022628"],"related_works":["https://openalex.org/W357196361","https://openalex.org/W2027314909","https://openalex.org/W3109425891","https://openalex.org/W3096637473","https://openalex.org/W1036938216","https://openalex.org/W2113714434","https://openalex.org/W2319693127","https://openalex.org/W2377792686","https://openalex.org/W829658220","https://openalex.org/W2740316168"],"abstract_inverted_index":{"In":[0],"this":[1],"research,":[2],"the":[3,8,17,45,51,61,70,78,84,91,99],"fourth":[4],"axiom":[5],"to":[6,58],"improve":[7],"well-defined":[9],"examination":[10],"of":[11,29,72,93],"similarity":[12,33,65,81,104],"measures":[13,18,34,105],"is":[14,67],"studied,":[15],"where":[16],"have":[19],"a":[20,26,39],"symmetric":[21,107],"structure.":[22],"We":[23],"first":[24],"provide":[25],"theoretic":[27],"enhancement":[28],"three":[30],"correlation":[31,63,79],"coefficient":[32,64,80],"that":[35,60,77],"were":[36],"proposed":[37,49],"by":[38,50],"source":[40,52],"paper.":[41],"Second,":[42],"we":[43,75],"use":[44],"same":[46],"numerical":[47],"example":[48],"paper":[53],"for":[54],"pattern":[55],"recognition":[56],"problems":[57,102],"illustrate":[59],"weighted":[62],"measure":[66,82],"dependent":[68],"on":[69],"set":[71,87],"weights.":[73],"Finally,":[74],"demonstrate":[76],"in":[83],"intuitionistic":[85],"fuzzy":[86],"environment":[88],"can":[89],"address":[90],"issue":[92],"practical":[94],"fault":[95],"diagnosis":[96],"when":[97],"solving":[98],"turbine":[100],"engine":[101],"using":[103],"with":[106],"characteristics.":[108]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}