{"id":"https://openalex.org/W1761432600","doi":"https://doi.org/10.1080/00207721.2015.1036476","title":"Hesitant fuzzy information measures and their applications in multi-criteria decision making","display_name":"Hesitant fuzzy information measures and their applications in multi-criteria decision making","publication_year":2015,"publication_date":"2015-05-13","ids":{"openalex":"https://openalex.org/W1761432600","doi":"https://doi.org/10.1080/00207721.2015.1036476","mag":"1761432600"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2015.1036476","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2015.1036476","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101758409","display_name":"Junhua Hu","orcid":"https://orcid.org/0000-0002-8879-4970"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junhua Hu","raw_affiliation_strings":["School of Business, Central South University, Changsha Hunan, China","School of Business, Central South University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha Hunan, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Business, Central South University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080765061","display_name":"Xiaolong Zhang","orcid":"https://orcid.org/0000-0002-6828-4930"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaolong Zhang","raw_affiliation_strings":["School of Business, Central South University, Changsha Hunan, China","School of Business, Central South University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha Hunan, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Business, Central South University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100373745","display_name":"Xiaohong Chen","orcid":"https://orcid.org/0000-0002-9797-8384"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohong Chen","raw_affiliation_strings":["School of Business, Central South University, Changsha Hunan, China","School of Business, Central South University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha Hunan, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Business, Central South University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100737217","display_name":"Yongmei Liu","orcid":"https://orcid.org/0000-0002-0139-5900"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongmei Liu","raw_affiliation_strings":["School of Business, Central South University, Changsha Hunan, China","School of Business, Central South University, Changsha, Hunan, China"],"affiliations":[{"raw_affiliation_string":"School of Business, Central South University, Changsha Hunan, China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Business, Central South University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101758409"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":10.0153,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.98129794,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"47","issue":"1","first_page":"62","last_page":"76"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9689000248908997,"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/T11634","display_name":"Water Quality and Pollution Assessment","score":0.9399999976158142,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5735942125320435},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.5672383904457092},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.559476912021637},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5431475043296814},{"id":"https://openalex.org/keywords/topsis","display_name":"TOPSIS","score":0.5430748462677002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4855155944824219},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.43998515605926514},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.437104195356369},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43511703610420227},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.42483651638031006},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3801540434360504},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3767964541912079},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.27389365434646606}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5735942125320435},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.5672383904457092},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.559476912021637},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5431475043296814},{"id":"https://openalex.org/C51566761","wikidata":"https://www.wikidata.org/wiki/Q1235853","display_name":"TOPSIS","level":2,"score":0.5430748462677002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4855155944824219},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.43998515605926514},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.437104195356369},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43511703610420227},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.42483651638031006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3801540434360504},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3767964541912079},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.27389365434646606},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2015.1036476","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2015.1036476","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:47:y:2016:i:1:p:62-76","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2015.1036476","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2300438924","display_name":null,"funder_award_id":"71371196","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4202076506","display_name":null,"funder_award_id":"71221061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5379060174","display_name":null,"funder_award_id":"71431006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6621436126","display_name":null,"funder_award_id":"71210003","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":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W26772505","https://openalex.org/W145213067","https://openalex.org/W194786220","https://openalex.org/W294994052","https://openalex.org/W1529762651","https://openalex.org/W1584722645","https://openalex.org/W1816134045","https://openalex.org/W1965239040","https://openalex.org/W1966790966","https://openalex.org/W1966808269","https://openalex.org/W1969482876","https://openalex.org/W1972073558","https://openalex.org/W1980036384","https://openalex.org/W1980564456","https://openalex.org/W1983720898","https://openalex.org/W1987177581","https://openalex.org/W1991419869","https://openalex.org/W1996697778","https://openalex.org/W1996937753","https://openalex.org/W2000763566","https://openalex.org/W2002574279","https://openalex.org/W2007877401","https://openalex.org/W2010191074","https://openalex.org/W2014417436","https://openalex.org/W2016236227","https://openalex.org/W2022546473","https://openalex.org/W2029074979","https://openalex.org/W2038190934","https://openalex.org/W2040121225","https://openalex.org/W2041210202","https://openalex.org/W2041455711","https://openalex.org/W2048394994","https://openalex.org/W2050090718","https://openalex.org/W2062870022","https://openalex.org/W2063170755","https://openalex.org/W2067442047","https://openalex.org/W2067648457","https://openalex.org/W2074922760","https://openalex.org/W2083199031","https://openalex.org/W2083798655","https://openalex.org/W2091130862","https://openalex.org/W2091275864","https://openalex.org/W2099469179","https://openalex.org/W2116365436","https://openalex.org/W2131390763","https://openalex.org/W2157041604","https://openalex.org/W2163826446","https://openalex.org/W2167967165","https://openalex.org/W2170853747","https://openalex.org/W2506768821","https://openalex.org/W2598771954","https://openalex.org/W2912565176","https://openalex.org/W3156834475","https://openalex.org/W4210259099","https://openalex.org/W4211007335","https://openalex.org/W4245152641","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2121560876","https://openalex.org/W2253053392","https://openalex.org/W2184441312","https://openalex.org/W4206081075","https://openalex.org/W2331106272","https://openalex.org/W2366385051","https://openalex.org/W1470403688","https://openalex.org/W1486684451","https://openalex.org/W4361984403","https://openalex.org/W4361273540"],"abstract_inverted_index":{"Hesitant":[0],"fuzzy":[1,47,51,60,75,112],"set":[2],"(HFS)":[3],"is":[4,22,43,114,134],"a":[5,38,107,131],"powerful":[6],"decision":[7,128],"tool":[8],"to":[9,23,124,136],"express":[10],"uncertain":[11],"information":[12,27,98,105,113],"more":[13,25,143],"flexibly":[14],"and":[15,49,68,86,130,145],"comprehensively.":[16],"The":[17],"aim":[18],"of":[19,40,81],"this":[20],"paper":[21],"propose":[24],"reasonable":[26],"measures":[28,42,54,88,141],"for":[29,45,110],"HFSs":[30],"in":[31,122,147],"comparison":[32],"with":[33,77],"the":[34,64,73,78,93,97,103,126,139],"existing":[35],"ones.":[36],"First,":[37],"series":[39],"distance":[41],"suggested":[44,140],"hesitant":[46,50,59,74,111],"element":[48,76],"sets.":[52],"These":[53],"are":[55,89,120,142],"directly":[56],"calculated":[57],"from":[58],"elements":[61],"without":[62],"judging":[63],"decision-makers\u2019":[65],"risk":[66],"preference":[67],"adding":[69],"any":[70],"values":[71],"into":[72],"smaller":[79],"number":[80],"elements.":[82],"Then,":[83],"some":[84,117],"similarity":[85],"entropy":[87],"proposed":[90,104,127],"based":[91,101],"on":[92,102],"transforming":[94],"relationship":[95],"among":[96],"measures.":[99],"Additionally,":[100],"measures,":[106],"TOPSIS":[108],"method":[109,129],"provided.":[115],"Finally,":[116],"numerical":[118],"examples":[119],"used":[121],"order":[123],"illustrate":[125],"comparative":[132],"analysis":[133],"made":[135],"demonstrate":[137],"that":[138],"objective":[144],"feasible":[146],"certain":[148],"cases.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}