{"id":"https://openalex.org/W4365509013","doi":"https://doi.org/10.3390/axioms12040376","title":"Distance Measures Based on Metric Information Matrix for Atanassov\u2019s Intuitionistic Fuzzy Sets","display_name":"Distance Measures Based on Metric Information Matrix for Atanassov\u2019s Intuitionistic Fuzzy Sets","publication_year":2023,"publication_date":"2023-04-14","ids":{"openalex":"https://openalex.org/W4365509013","doi":"https://doi.org/10.3390/axioms12040376"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12040376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040376","pdf_url":"https://www.mdpi.com/2075-1680/12/4/376/pdf?version=1681480887","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/2075-1680/12/4/376/pdf?version=1681480887","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039672587","display_name":"Wenjuan Ren","orcid":"https://orcid.org/0009-0009-2950-1224"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210137199","display_name":"Aerospace Information Research Institute","ror":"https://ror.org/0419fj215","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210137199"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenjuan Ren","raw_affiliation_strings":["Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"],"affiliations":[{"raw_affiliation_string":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210137199","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091305859","display_name":"Zhanpeng Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210137199","display_name":"Aerospace Information Research Institute","ror":"https://ror.org/0419fj215","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210137199"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhanpeng Yang","raw_affiliation_strings":["Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"],"affiliations":[{"raw_affiliation_string":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210137199","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102283144","display_name":"Li Xipeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xipeng Li","raw_affiliation_strings":["Systems Engineering Institute, Academy of Military Sciences, Beijing 100190, China"],"affiliations":[{"raw_affiliation_string":"Systems Engineering Institute, Academy of Military Sciences, Beijing 100190, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039672587","https://openalex.org/A5091305859"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210137199"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.3231,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80509839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"12","issue":"4","first_page":"376","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9983000159263611,"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":0.9939000010490417,"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/distance-matrix","display_name":"Distance matrix","score":0.7715167999267578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7492074370384216},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7386083602905273},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.7064798474311829},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6580681800842285},{"id":"https://openalex.org/keywords/distance-matrices-in-phylogeny","display_name":"Distance matrices in phylogeny","score":0.5971876978874207},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5469413995742798},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4521227180957794},{"id":"https://openalex.org/keywords/distance-measures","display_name":"Distance measures","score":0.43790918588638306},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.362528532743454},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19657906889915466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17313453555107117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1666610836982727},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.13305845856666565}],"concepts":[{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.7715167999267578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7492074370384216},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7386083602905273},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.7064798474311829},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6580681800842285},{"id":"https://openalex.org/C5349765","wikidata":"https://www.wikidata.org/wiki/Q5282866","display_name":"Distance matrices in phylogeny","level":2,"score":0.5971876978874207},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5469413995742798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4521227180957794},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.43790918588638306},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.362528532743454},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19657906889915466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17313453555107117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1666610836982727},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.13305845856666565},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12040376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040376","pdf_url":"https://www.mdpi.com/2075-1680/12/4/376/pdf?version=1681480887","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:doaj.org/article:9db81589f5d84eff84a62468a9033888","is_oa":true,"landing_page_url":"https://doaj.org/article/9db81589f5d84eff84a62468a9033888","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 12, Iss 4, p 376 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/4/376/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12040376","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 12; Issue 4; Pages: 376","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12040376","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040376","pdf_url":"https://www.mdpi.com/2075-1680/12/4/376/pdf?version=1681480887","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":[],"awards":[{"id":"https://openalex.org/G120232579","display_name":null,"funder_award_id":"Y2022052","funder_id":"https://openalex.org/F4320322847","funder_display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences"},{"id":"https://openalex.org/G1433131842","display_name":null,"funder_award_id":"6213101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2868273350","display_name":null,"funder_award_id":"202205","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G3472539505","display_name":null,"funder_award_id":"202205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4449054793","display_name":null,"funder_award_id":"Y2022052","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G5783530182","display_name":null,"funder_award_id":"62131019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320322847","display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","ror":"https://ror.org/031141b54"},{"id":"https://openalex.org/F4320335892","display_name":"Youth Innovation Promotion Association","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4365509013.pdf"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W624701991","https://openalex.org/W1177241668","https://openalex.org/W1980564456","https://openalex.org/W1989058043","https://openalex.org/W1995972849","https://openalex.org/W1996937753","https://openalex.org/W1998459953","https://openalex.org/W2011023980","https://openalex.org/W2019633123","https://openalex.org/W2031241748","https://openalex.org/W2043376473","https://openalex.org/W2056021265","https://openalex.org/W2065471531","https://openalex.org/W2070545443","https://openalex.org/W2086869454","https://openalex.org/W2093617335","https://openalex.org/W2094298237","https://openalex.org/W2097403045","https://openalex.org/W2138610292","https://openalex.org/W2146489275","https://openalex.org/W2167967165","https://openalex.org/W2196181906","https://openalex.org/W2205336636","https://openalex.org/W2208115510","https://openalex.org/W2208264322","https://openalex.org/W2258450904","https://openalex.org/W2343818608","https://openalex.org/W2548435430","https://openalex.org/W2587630422","https://openalex.org/W2610833308","https://openalex.org/W2754849094","https://openalex.org/W2771639180","https://openalex.org/W2775083246","https://openalex.org/W2789613617","https://openalex.org/W2799561996","https://openalex.org/W2888572347","https://openalex.org/W2902393417","https://openalex.org/W2903425833","https://openalex.org/W2903798166","https://openalex.org/W2951063129","https://openalex.org/W2963217065","https://openalex.org/W2983268957","https://openalex.org/W3095623965","https://openalex.org/W3215634724","https://openalex.org/W4211007335","https://openalex.org/W4223435940","https://openalex.org/W4302773455","https://openalex.org/W4316690390"],"related_works":["https://openalex.org/W1605858995","https://openalex.org/W4206923957","https://openalex.org/W4387171312","https://openalex.org/W3015876227","https://openalex.org/W2090844285","https://openalex.org/W2757023457","https://openalex.org/W2168156479","https://openalex.org/W2108613438","https://openalex.org/W2146092900","https://openalex.org/W3122168434"],"abstract_inverted_index":{"The":[0,72],"metric":[1,10,33,42,49,64,106],"matrix":[2,43,66,108],"theory":[3],"is":[4],"an":[5],"important":[6],"research":[7],"object":[8],"of":[9,23,37,63,100,121,129],"measure":[11,51,69,80],"geometry":[12],"and":[13],"it":[14],"can":[15,143],"be":[16],"used":[17],"to":[18,50,79,91,117,137],"characterize":[19],"the":[20,41,47,52,77,81,93,98,119,122,127,130,140],"geometric":[21],"structure":[22],"a":[24,61,104],"set.":[25],"For":[26],"intuitionistic":[27,86],"fuzzy":[28,87],"sets":[29],"(IFS),":[30],"we":[31,102],"defined":[32,103],"information":[34,65,94,107],"matrices":[35],"(MIM)":[36],"IFS":[38],"by":[39,97,110,148],"using":[40],"theory.":[44],"We":[45,58],"introduced":[46],"Gromov\u2013Hausdorff":[48],"distance":[53,67,74,82,109,124],"between":[54,83],"any":[55],"two":[56,84],"MIMs.":[57],"then":[59],"constructed":[60,123],"kind":[62],"knowledge":[68],"for":[70],"IFS.":[71,149],"proposed":[73,141],"measures":[75],"have":[76],"ability":[78],"incomplete":[85],"sets.":[88],"In":[89],"order":[90],"reduce":[92],"confusion":[95],"caused":[96],"disorder":[99],"MIM,":[101],"homogenous":[105],"rearranging":[111],"MIM.":[112],"Some":[113],"theorems":[114],"are":[115,135],"given":[116,136],"show":[118,138],"properties":[120],"measures.":[125],"At":[126],"end":[128],"paper,":[131],"some":[132],"numerical":[133],"experiments":[134],"that":[139],"distances":[142],"recognize":[144],"different":[145],"patterns":[146],"represented":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}