{"id":"https://openalex.org/W2899515532","doi":"https://doi.org/10.3390/sym10110557","title":"Novel Parameterized Distance Measures on Hesitant Fuzzy Sets with Credibility Degree and Their Application in Decision-Making","display_name":"Novel Parameterized Distance Measures on Hesitant Fuzzy Sets with Credibility Degree and Their Application in Decision-Making","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2899515532","doi":"https://doi.org/10.3390/sym10110557","mag":"2899515532"},"language":"en","primary_location":{"id":"doi:10.3390/sym10110557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110557","pdf_url":"https://www.mdpi.com/2073-8994/10/11/557/pdf?version=1541040662","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/2073-8994/10/11/557/pdf?version=1541040662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101874452","display_name":"Jiaru Li","orcid":"https://orcid.org/0000-0001-5812-4450"},"institutions":[{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaru Li","raw_affiliation_strings":["College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China","institution_ids":["https://openalex.org/I96733725"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106855783","display_name":"Fangwei Zhang","orcid":"https://orcid.org/0000-0001-5798-5662"},"institutions":[{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fangwei Zhang","raw_affiliation_strings":["College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China"],"raw_orcid":"https://orcid.org/0000-0001-5798-5662","affiliations":[{"raw_affiliation_string":"College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China","institution_ids":["https://openalex.org/I96733725"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100661438","display_name":"Qiang Li","orcid":"https://orcid.org/0009-0001-0614-5492"},"institutions":[{"id":"https://openalex.org/I4210145669","display_name":"Shanghai Police College","ror":"https://ror.org/0479fds27","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210145669"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Li","raw_affiliation_strings":["Faculty of Public Security, Shanghai Police College, Shanghai 200137, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Public Security, Shanghai Police College, Shanghai 200137, China","institution_ids":["https://openalex.org/I4210145669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101517359","display_name":"Jing Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":true,"raw_author_name":"Jing Sun","raw_affiliation_strings":["Department of Mathematics, University of Macau, Macau 999078, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Macau 999078, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038537627","display_name":"Janney Yee","orcid":"https://orcid.org/0000-0002-4467-9671"},"institutions":[{"id":"https://openalex.org/I3133184724","display_name":"University College Birmingham","ror":"https://ror.org/042ver755","country_code":"GB","type":"education","lineage":["https://openalex.org/I3133184724"]},{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Janney Yee","raw_affiliation_strings":["College of Social Sciences, University of Birmingham, Birmingham 1610681, UK"],"raw_orcid":"https://orcid.org/0000-0002-4467-9671","affiliations":[{"raw_affiliation_string":"College of Social Sciences, University of Birmingham, Birmingham 1610681, UK","institution_ids":["https://openalex.org/I3133184724","https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100599251","display_name":"Shuhong Wang","orcid":"https://orcid.org/0000-0002-5251-8704"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Shuhong Wang","raw_affiliation_strings":["Shool of Computing, National University of Singapore, Singapore 118414, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shool of Computing, National University of Singapore, Singapore 118414, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004654656","display_name":"Shujun Xiao","orcid":null},"institutions":[{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujun Xiao","raw_affiliation_strings":["Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China","institution_ids":["https://openalex.org/I96733725"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5101517359","https://openalex.org/A5106855783"],"corresponding_institution_ids":["https://openalex.org/I204512498","https://openalex.org/I96733725"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6605,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75254237,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"10","issue":"11","first_page":"557","last_page":"557"},"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":0.9581000208854675,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9372000098228455,"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/credibility","display_name":"Credibility","score":0.661582350730896},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6257753968238831},{"id":"https://openalex.org/keywords/distance-measures","display_name":"Distance measures","score":0.619979202747345},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5800491571426392},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5729511976242065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5707993507385254},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5456505417823792},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.4907037019729614},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4202175736427307},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4198925495147705},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.41835668683052063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4148111045360565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33401256799697876},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2748357951641083},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19840717315673828}],"concepts":[{"id":"https://openalex.org/C2780224610","wikidata":"https://www.wikidata.org/wiki/Q1530061","display_name":"Credibility","level":2,"score":0.661582350730896},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6257753968238831},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.619979202747345},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5800491571426392},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5729511976242065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5707993507385254},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5456505417823792},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.4907037019729614},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4202175736427307},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4198925495147705},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41835668683052063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4148111045360565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33401256799697876},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2748357951641083},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19840717315673828},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym10110557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110557","pdf_url":"https://www.mdpi.com/2073-8994/10/11/557/pdf?version=1541040662","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:scholarbank.nus.edu.sg:10635/210860","is_oa":true,"landing_page_url":"https://scholarbank.nus.edu.sg/handle/10635/210860","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus OA2018","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:e68ba6fe63fd4ab0b9eb413440cc59fb","is_oa":true,"landing_page_url":"https://doaj.org/article/e68ba6fe63fd4ab0b9eb413440cc59fb","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 10, Iss 11, p 557 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/11/557/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym10110557","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/sym10110557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10110557","pdf_url":"https://www.mdpi.com/2073-8994/10/11/557/pdf?version=1541040662","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":[{"score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G6097581728","display_name":null,"funder_award_id":"51508319","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2899515532.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1731455596","https://openalex.org/W1972591816","https://openalex.org/W1980564456","https://openalex.org/W1983343002","https://openalex.org/W1984502995","https://openalex.org/W1991419869","https://openalex.org/W1991482489","https://openalex.org/W2001201684","https://openalex.org/W2023671427","https://openalex.org/W2064974864","https://openalex.org/W2089807790","https://openalex.org/W2116365436","https://openalex.org/W2157041604","https://openalex.org/W2167967165","https://openalex.org/W2179281014","https://openalex.org/W2744824089","https://openalex.org/W2809929944","https://openalex.org/W3143689354","https://openalex.org/W4211007335","https://openalex.org/W4233428539","https://openalex.org/W4240278385","https://openalex.org/W4245152641","https://openalex.org/W4292078529","https://openalex.org/W6679780668"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W2010458966","https://openalex.org/W1768512366","https://openalex.org/W1486684451","https://openalex.org/W2116249946","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W4317826560"],"abstract_inverted_index":{"The":[0],"subject":[1],"of":[2,10,12,42,70,117,131],"this":[3,107],"study":[4,108],"is":[5,123,137],"to":[6,78,97,114],"explore":[7],"the":[8,60,63,67,110,118,129,132],"role":[9],"cardinality":[11],"hesitant":[13,21,71],"fuzzy":[14,22,72],"element":[15,68],"(HFE)":[16],"in":[17,120],"distance":[18,44,57,135],"measures":[19,45,58,136],"on":[20,46],"sets":[23],"(HFSs).":[24],"Firstly,":[25],"three":[26,52,103],"parameters,":[27],"i.e.,":[28],"credibility":[29,116],"factor,":[30,32],"conservative":[31],"and":[33,66,75,81],"a":[34,40,115],"risk":[35,93],"factor":[36],"are":[37,48,76,95],"introduced,":[38],"thereafter,":[39],"series":[41],"novel":[43],"HFSs":[47],"proposed":[49,56,134],"using":[50,86],"these":[51,87,102],"parameters.":[53,104],"These":[54],"newly":[55,133],"handle":[59],"relationship":[61],"between":[62],"cardinal":[64],"number":[65],"values":[69,100,119],"set":[73],"well,":[74],"suitable":[77],"combine":[79],"subjective":[80],"objective":[82],"decision-making":[83],"information.":[84],"When":[85],"functions,":[88],"decision":[89],"makers":[90],"with":[91,125],"different":[92,99],"preferences":[94],"allowed":[96],"give":[98],"for":[101],"In":[105],"particular,":[106],"transfers":[109],"hesitance":[111],"degree":[112],"index":[113],"HFEs,":[121],"which":[122],"consistent":[124],"people\u2019s":[126],"intuition.":[127],"Finally,":[128],"practicability":[130],"verified":[138],"by":[139],"two":[140],"examples.":[141]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}