{"id":"https://openalex.org/W2892785338","doi":"https://doi.org/10.3390/sym10100429","title":"New Distance Measure for Atanassov\u2019s Intuitionistic Fuzzy Sets and Its Application in Decision Making","display_name":"New Distance Measure for Atanassov\u2019s Intuitionistic Fuzzy Sets and Its Application in Decision Making","publication_year":2018,"publication_date":"2018-09-22","ids":{"openalex":"https://openalex.org/W2892785338","doi":"https://doi.org/10.3390/sym10100429","mag":"2892785338"},"language":"en","primary_location":{"id":"doi:10.3390/sym10100429","doi":"https://doi.org/10.3390/sym10100429","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10100429","pdf_url":"https://www.mdpi.com/2073-8994/10/10/429/pdf?version=1537942793","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/10/429/pdf?version=1537942793","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Di Ke","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Di Ke","raw_affiliation_strings":["School of Business, Nankai University, Tianjin 300071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business, Nankai University, Tianjin 300071, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100784138","display_name":"Yafei Song","orcid":"https://orcid.org/0000-0003-0962-0671","observed_orcids":["https://orcid.org/0000-0003-0962-0671","https://orcid.org/0009-0004-6952-1071"]},"institutions":[{"id":"https://openalex.org/I4210104252","display_name":"Air Force Engineering University","ror":"https://ror.org/00seraz22","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210104252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yafei Song","raw_affiliation_strings":["College of Air and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Air and Missile Defense, Air Force Engineering University, Xi\u2019an 710051, China","institution_ids":["https://openalex.org/I4210104252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100683600","display_name":"Quan Wen","orcid":"https://orcid.org/0000-0001-8899-2291","observed_orcids":["https://orcid.org/0000-0001-8899-2291"]},"institutions":[{"id":"https://openalex.org/I4210104252","display_name":"Air Force Engineering University","ror":"https://ror.org/00seraz22","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210104252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Quan","raw_affiliation_strings":["College of Air Traffic Control and Navigation, Air Force Engineering University, Xi\u2019an 710051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Air Traffic Control and Navigation, Air Force Engineering University, Xi\u2019an 710051, China","institution_ids":["https://openalex.org/I4210104252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100784138"],"corresponding_institution_ids":["https://openalex.org/I4210104252"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":2.6672,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.90242711,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"10","issue":"10","first_page":"429","last_page":"429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9735999703407288,"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":0.9735999703407288,"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":0.023099999874830246,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/atanassov-s-intuitionistic-fuzzy-sets","display_name":"Atanassov's intuitionistic fuzzy sets","score":0.9539999961853027},{"id":"https://openalex.org/keywords/distance-metrics","display_name":"distance measures","score":0.9319999814033508},{"id":"https://openalex.org/keywords/similarity-measures","display_name":"similarity measures","score":0.7540000081062317},{"id":"https://openalex.org/keywords/interval-valued-fuzzy-sets","display_name":"interval-valued fuzzy sets","score":0.9490000009536743},{"id":"https://openalex.org/keywords/axiomatic-properties","display_name":"axiomatic properties","score":0.8960000276565552},{"id":"https://openalex.org/keywords/multi-attribute-decision-making","display_name":"multi-attribute decision making","score":0.9900000095367432},{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.8159999847412109},{"id":"https://openalex.org/keywords/uncertainty-representation","display_name":"uncertainty representation","score":0.3619999885559082}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7913633584976196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6736524701118469},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.6174470782279968},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.5794954299926758},{"id":"https://openalex.org/C2776517306","wikidata":"https://www.wikidata.org/wiki/Q29017317","display_name":"Similarity measure","level":2,"score":0.5574931502342224},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.47499290108680725},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.46627214550971985},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4177316427230835},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4129672646522522},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.36576855182647705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35364553332328796},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3150360584259033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3104669451713562},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2976364195346832},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14221903681755066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08525320887565613},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym10100429","doi":"https://doi.org/10.3390/sym10100429","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10100429","pdf_url":"https://www.mdpi.com/2073-8994/10/10/429/pdf?version=1537942793","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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:4cbc7d66d4f04344900dd91ae22a5be2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/4cbc7d66d4f04344900dd91ae22a5be2","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,"listed_in":[],"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 10, Iss 10, p 429 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym10100429","doi":"https://doi.org/10.3390/sym10100429","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10100429","pdf_url":"https://www.mdpi.com/2073-8994/10/10/429/pdf?version=1537942793","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2017348484","display_name":null,"funder_award_id":"61703426, 61273275, 61806219,  61876189 , 61503407","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2952667752","display_name":null,"funder_award_id":"61876189","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3006619586","display_name":null,"funder_award_id":"61703426","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5092255126","display_name":null,"funder_award_id":"61503407","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5204689012","display_name":null,"funder_award_id":"61273275","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5242311573","display_name":null,"funder_award_id":"61806219","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2892785338.pdf","grobid_xml":"https://content.openalex.org/works/W2892785338.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1816134045","https://openalex.org/W1969921454","https://openalex.org/W1975061798","https://openalex.org/W1980564456","https://openalex.org/W1980748255","https://openalex.org/W1981107087","https://openalex.org/W1981963907","https://openalex.org/W1982618675","https://openalex.org/W1986813400","https://openalex.org/W1998274657","https://openalex.org/W2003243224","https://openalex.org/W2015282411","https://openalex.org/W2029377923","https://openalex.org/W2039791408","https://openalex.org/W2043376473","https://openalex.org/W2044313855","https://openalex.org/W2055108933","https://openalex.org/W2067648457","https://openalex.org/W2070417014","https://openalex.org/W2079767857","https://openalex.org/W2080321857","https://openalex.org/W2081037298","https://openalex.org/W2087501680","https://openalex.org/W2089118061","https://openalex.org/W2091275864","https://openalex.org/W2099469179","https://openalex.org/W2113693055","https://openalex.org/W2116208597","https://openalex.org/W2144086263","https://openalex.org/W2273432898","https://openalex.org/W2293737317","https://openalex.org/W2410679497","https://openalex.org/W2753546593","https://openalex.org/W2765227114","https://openalex.org/W2801882539","https://openalex.org/W2802256656","https://openalex.org/W2810040988","https://openalex.org/W4211007335","https://openalex.org/W4256089154","https://openalex.org/W4292078529"],"related_works":["https://openalex.org/W4414561800","https://openalex.org/W2972484360","https://openalex.org/W280010694","https://openalex.org/W4399555680","https://openalex.org/W3005314970","https://openalex.org/W3012472501","https://openalex.org/W7217672909","https://openalex.org/W4224308303","https://openalex.org/W2153868331","https://openalex.org/W4377008699"],"abstract_inverted_index":{"The":[0,94,125],"intuitionistic":[1,24,43,64],"fuzzy":[2,16,25,44,65,92],"set":[3,26],"introduced":[4],"by":[5,152],"Atanassov":[6],"has":[7],"greater":[8],"ability":[9],"in":[10,108],"depicting":[11],"and":[12,30,40,59,84,159,186,191],"handling":[13],"uncertainty.":[14],"Intuitionistic":[15],"measure":[17,29,32,55,71,80,101,116,131,183],"is":[18,74,117,132,143,184],"an":[19,52,155],"important":[20],"research":[21],"area":[22],"of":[23,42,51,81,97,127,194],"theory.":[27],"Distance":[28],"similarity":[31,153],"are":[33,102],"two":[34],"complementary":[35],"concepts":[36],"quantifying":[37],"the":[38,49,85,98,113,121,128,147,160,168,180],"difference":[39,122],"closeness":[41],"sets.":[45,93],"This":[46,177],"paper":[47],"addresses":[48],"definition":[50],"effective":[53,185],"distance":[54,70,79,100,115,130,162,182],"with":[56],"concise":[57],"form":[58],"specific":[60],"meaning":[61],"for":[62,72,138,149],"Atanassov\u2019s":[63],"sets":[66],"(AIFSs).":[67],"A":[68,135],"new":[69,99,114,129,136,161,181],"AIFSs":[73,88],"defined":[75],"based":[76,107,145],"on":[77,146],"a":[78],"interval":[82,90],"values":[83],"transformation":[86],"from":[87,188],"to":[89,119,154],"valued":[91],"axiomatic":[95],"properties":[96],"mathematically":[103],"investigated.":[104],"Comparative":[105],"analysis":[106],"numerical":[109],"examples":[110],"indicates":[111],"that":[112,167,179],"competent":[118],"quantify":[120],"between":[123],"AIFSs.":[124],"application":[126],"also":[133],"discussed.":[134],"method":[137,158,171],"multi-attribute":[139],"decision":[140],"making":[141],"(MADM)":[142],"developed":[144,169],"technique":[148],"order":[150],"preference":[151,175],"ideal":[156],"solution":[157],"measure.":[163],"Numerical":[164],"applications":[165],"indicate":[166],"MADM":[170],"can":[172],"obtain":[173],"reasonable":[174],"orders.":[176],"shows":[178],"rational":[187],"both":[189],"mathematical":[190],"practical":[192],"points":[193],"view.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2018-10-05T00:00:00"}