{"id":"https://openalex.org/W2943061904","doi":"https://doi.org/10.1109/access.2019.2914703","title":"Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty","display_name":"Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2943061904","doi":"https://doi.org/10.1109/access.2019.2914703","mag":"2943061904"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2914703","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2914703","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08705220.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08705220.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040477292","display_name":"Ting\u2010Yu Chen","orcid":"https://orcid.org/0000-0002-2171-4139"},"institutions":[{"id":"https://openalex.org/I4210116208","display_name":"Linkou Chang Gung Memorial Hospital","ror":"https://ror.org/02dnn6q67","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I3020100970","https://openalex.org/I4210116208"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Ting-Yu Chen","raw_affiliation_strings":["Department of Nursing, Linkou Chang Gung Memorial Hospital, Taoyuan, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-2171-4139","affiliations":[{"raw_affiliation_string":"Department of Nursing, Linkou Chang Gung Memorial Hospital, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I4210116208"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040477292"],"corresponding_institution_ids":["https://openalex.org/I4210116208"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.3872,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92280466,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"58168","last_page":"58185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9929999709129333,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.967199981212616,"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/distance-measures","display_name":"Distance measures","score":0.7588316798210144},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.7218159437179565},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.7040383219718933},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6930539608001709},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.641358494758606},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.593986988067627},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.5697649717330933},{"id":"https://openalex.org/keywords/compromise","display_name":"Compromise","score":0.5469378232955933},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.538019061088562},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4922996759414673},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.48321783542633057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4393169581890106},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37586262822151184},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.302300363779068},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2309829592704773}],"concepts":[{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.7588316798210144},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.7218159437179565},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.7040383219718933},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6930539608001709},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.641358494758606},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.593986988067627},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.5697649717330933},{"id":"https://openalex.org/C46355384","wikidata":"https://www.wikidata.org/wiki/Q726686","display_name":"Compromise","level":2,"score":0.5469378232955933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.538019061088562},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4922996759414673},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.48321783542633057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4393169581890106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37586262822151184},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.302300363779068},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2309829592704773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2914703","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2914703","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08705220.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6776288d571f472f8cee4193fc5bc357","is_oa":true,"landing_page_url":"https://doaj.org/article/6776288d571f472f8cee4193fc5bc357","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":"IEEE Access, Vol 7, Pp 58168-58185 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2914703","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2914703","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08705220.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6100000143051147}],"awards":[{"id":"https://openalex.org/G5045356945","display_name":null,"funder_award_id":"BMRP 574","funder_id":"https://openalex.org/F4320313619","funder_display_name":"Chang Gung Memorial Hospital"},{"id":"https://openalex.org/G5276173164","display_name":null,"funder_award_id":"CMRPD2F0203","funder_id":"https://openalex.org/F4320313619","funder_display_name":"Chang Gung Memorial Hospital"},{"id":"https://openalex.org/G6281320475","display_name":"Using a Mixed Choice Strategy to Develop Compromising Decision-Making Models for Multiple Criteria Decision Analysis Within the Interval-Valued Intuitionistic Fuzzy Environment","funder_award_id":"MOST105-2410-H182-007-MY3","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"}],"funders":[{"id":"https://openalex.org/F4320313619","display_name":"Chang Gung Memorial Hospital","ror":"https://ror.org/02verss31"},{"id":"https://openalex.org/F4320322767","display_name":"Chang Gung Medical Foundation","ror":"https://ror.org/02verss31"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2943061904.pdf","grobid_xml":"https://content.openalex.org/works/W2943061904.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W802649050","https://openalex.org/W1668569279","https://openalex.org/W1829951598","https://openalex.org/W2013932252","https://openalex.org/W2065109455","https://openalex.org/W2184989861","https://openalex.org/W2292359941","https://openalex.org/W2346494717","https://openalex.org/W2412590235","https://openalex.org/W2506768821","https://openalex.org/W2593530789","https://openalex.org/W2722833530","https://openalex.org/W2751818504","https://openalex.org/W2752015533","https://openalex.org/W2753862205","https://openalex.org/W2756107921","https://openalex.org/W2784166218","https://openalex.org/W2801515029","https://openalex.org/W2808106811","https://openalex.org/W2811195812","https://openalex.org/W2883368008","https://openalex.org/W2885218772","https://openalex.org/W2885303467","https://openalex.org/W2890096933","https://openalex.org/W2891138446","https://openalex.org/W2895980456","https://openalex.org/W2896010100","https://openalex.org/W2897871005","https://openalex.org/W2899410322","https://openalex.org/W2900128988","https://openalex.org/W2900267418","https://openalex.org/W2902861753","https://openalex.org/W2904468863","https://openalex.org/W2915522475","https://openalex.org/W2919513668","https://openalex.org/W2922422072","https://openalex.org/W6653793587"],"related_works":["https://openalex.org/W2129888254","https://openalex.org/W2115336194","https://openalex.org/W4285132560","https://openalex.org/W1563946824","https://openalex.org/W4389080932","https://openalex.org/W2623629395","https://openalex.org/W4312786632","https://openalex.org/W3009108","https://openalex.org/W2300277393","https://openalex.org/W4256576878"],"abstract_inverted_index":{"This":[0],"paper":[1,90,157],"aims":[2],"at":[3],"developing":[4],"a":[5,17,36,102,139,159,183],"novel":[6],"generalized":[7,103],"distance":[8,58,93,104,129,152,201],"measure":[9,59,105],"of":[10,32,39,81,125,149,175,214,228],"Pythagorean":[11,33,61,112],"fuzzy":[12,41],"(PF)":[13],"sets":[14,83],"and":[15,87,98,101,115,122,137,173,195,205,234],"constructing":[16],"distance-based":[18],"compromise":[19,161,220],"approach":[20,162,178,221],"for":[21,46,60,111,116,163,243],"multiple":[22],"criteria":[23],"decision":[24,232],"analysis":[25],"(MCDA)":[26],"within":[27],"PF":[28,74,82,117,128,169,200],"environments.":[29],"The":[30,57,171],"theory":[31],"fuzziness":[34],"provides":[35],"representative":[37],"model":[38],"nonstandard":[40],"sets;":[42],"it":[43,67],"is":[44,64,107],"valuable":[45],"representing":[47],"complex":[48],"vague":[49],"or":[50],"imprecise":[51],"information":[52],"in":[53,154,209,230],"many":[54],"practical":[55],"applications.":[56],"membership":[62,113],"grades":[63,114],"important":[65],"because":[66],"can":[68,222],"effectively":[69,235],"quantify":[70],"the":[71,78,120,126,147,150,176,192,198,211,218,224,237],"separation":[72],"between":[73],"information.":[75,170,216],"Based":[76],"on":[77,109,186],"essential":[79],"characteristics":[80],"(membership,":[84],"non-membership,":[85],"strength,":[86],"direction),":[88],"this":[89,156],"proposes":[91],"several":[92],"measures,":[94],"namely,":[95],"new":[96],"Hamming":[97],"Euclidean":[99],"distances":[100],"that":[106,167],"based":[108],"them":[110],"sets.":[118],"Moreover,":[119],"useful":[121],"desirable":[123],"properties":[124],"proposed":[127,151,199],"measures":[130,153,202],"are":[131,179,203],"investigated":[132],"to":[133,145,191],"evaluate":[134,146],"their":[135],"advantages":[136],"form":[138],"solid":[140],"theoretical":[141],"basis.":[142],"In":[143],"addition,":[144],"performance":[148],"practice,":[155],"establishes":[158],"PF-distance-based":[160,219],"addressing":[164],"MCDA":[165,246],"problems":[166],"involve":[168],"effectiveness":[172],"practicability":[174],"developed":[177],"further":[180],"evaluated":[181],"through":[182],"case":[184],"study":[185],"bridge-superstructure":[187],"construction":[188],"methods.":[189],"According":[190],"application":[193],"results":[194],"comparative":[196],"analysis,":[197],"accurate":[204],"outperform":[206],"other":[207],"methods":[208],"handling":[210],"inherent":[212],"uncertainties":[213],"evaluation":[215],"Furthermore,":[217],"accommodate":[223],"much":[225],"higher":[226],"degrees":[227],"uncertainty":[229],"real-life":[231],"scenarios":[233],"determine":[236],"priority":[238],"ranking":[239],"among":[240],"candidate":[241],"alternatives":[242],"managing":[244],"complicated":[245],"problems.":[247]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
