{"id":"https://openalex.org/W2897005736","doi":"https://doi.org/10.1109/access.2018.2876403","title":"Group Decision Making With Probabilistic Hesitant Multiplicative Preference Relations Based on Consistency and Consensus","display_name":"Group Decision Making With Probabilistic Hesitant Multiplicative Preference Relations Based on Consistency and Consensus","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2897005736","doi":"https://doi.org/10.1109/access.2018.2876403","mag":"2897005736"},"language":"en","primary_location":{"id":"doi:10.1109/access.2018.2876403","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876403","pdf_url":null,"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://doi.org/10.1109/access.2018.2876403","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101851003","display_name":"Ming\u2010Wei Lin","orcid":"https://orcid.org/0000-0003-2026-7178"},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingwei Lin","raw_affiliation_strings":["Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-2026-7178","affiliations":[{"raw_affiliation_string":"Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, China","institution_ids":["https://openalex.org/I111753288"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086583180","display_name":"Qianshan Zhan","orcid":null},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qianshan Zhan","raw_affiliation_strings":["Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring, Fujian Normal University, Fuzhou, China","institution_ids":["https://openalex.org/I111753288"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeshui Xu","raw_affiliation_strings":["Business School, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Business School, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076921272","display_name":"Riqing Chen","orcid":"https://orcid.org/0000-0001-7828-550X"},"institutions":[{"id":"https://openalex.org/I61057504","display_name":"Fujian Agriculture and Forestry University","ror":"https://ror.org/04kx2sy84","country_code":"CN","type":"education","lineage":["https://openalex.org/I61057504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Riqing Chen","raw_affiliation_strings":["Digital Fujian Institute of the Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Digital Fujian Institute of the Big Data for Agriculture and Forestry, Fujian Agriculture and Forestry University, Fuzhou, China","institution_ids":["https://openalex.org/I61057504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101851003"],"corresponding_institution_ids":["https://openalex.org/I111753288"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.7422,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.93397911,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"6","issue":null,"first_page":"63329","last_page":"63344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9598000049591064,"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/consistency","display_name":"Consistency (knowledge bases)","score":0.7773224115371704},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7180873155593872},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.7129505276679993},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.705443263053894},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6751258969306946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5860474705696106},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5740853548049927},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4544444978237152},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.412004679441452},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38372519612312317},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38104140758514404},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3468605577945709},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.34396877884864807},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2969026565551758},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18941372632980347}],"concepts":[{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.7773224115371704},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7180873155593872},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.7129505276679993},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.705443263053894},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6751258969306946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5860474705696106},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5740853548049927},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4544444978237152},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.412004679441452},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38372519612312317},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38104140758514404},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3468605577945709},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34396877884864807},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2969026565551758},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18941372632980347},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2018.2876403","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876403","pdf_url":null,"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:077dd35a62d3424099100394de253563","is_oa":true,"landing_page_url":"https://doaj.org/article/077dd35a62d3424099100394de253563","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 6, Pp 63329-63344 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2018.2876403","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2018.2876403","pdf_url":null,"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":[{"score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1210102314","display_name":null,"funder_award_id":"2016J05149","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G6925082703","display_name":null,"funder_award_id":"61672157","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G804834654","display_name":null,"funder_award_id":"61872086","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/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null},{"id":"https://openalex.org/F4320335877","display_name":"Distinguished Young Scientific Research Talents Plan in Universities of Fujian Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1580198325","https://openalex.org/W2001482754","https://openalex.org/W2002226861","https://openalex.org/W2009530833","https://openalex.org/W2012491224","https://openalex.org/W2020221628","https://openalex.org/W2020407132","https://openalex.org/W2027218152","https://openalex.org/W2047161103","https://openalex.org/W2050203067","https://openalex.org/W2060589859","https://openalex.org/W2061532302","https://openalex.org/W2065209593","https://openalex.org/W2069403107","https://openalex.org/W2089336319","https://openalex.org/W2094625194","https://openalex.org/W2504040100","https://openalex.org/W2511415659","https://openalex.org/W2517223288","https://openalex.org/W2528793344","https://openalex.org/W2547954472","https://openalex.org/W2549088488","https://openalex.org/W2572810636","https://openalex.org/W2596318472","https://openalex.org/W2617807095","https://openalex.org/W2624050692","https://openalex.org/W2624554840","https://openalex.org/W2731891637","https://openalex.org/W2734293904","https://openalex.org/W2734645625","https://openalex.org/W2735550596","https://openalex.org/W2760428913","https://openalex.org/W2766025801","https://openalex.org/W2778309520","https://openalex.org/W2780422392","https://openalex.org/W2785666428","https://openalex.org/W2792164783","https://openalex.org/W2792671092","https://openalex.org/W2795795179","https://openalex.org/W2800565128","https://openalex.org/W2802256656","https://openalex.org/W2803843875","https://openalex.org/W2895743780"],"related_works":["https://openalex.org/W4205262062","https://openalex.org/W2002629668","https://openalex.org/W181477314","https://openalex.org/W2069750915","https://openalex.org/W2289408543","https://openalex.org/W2378292265","https://openalex.org/W2079781595","https://openalex.org/W59299519","https://openalex.org/W2804133259","https://openalex.org/W1969840038"],"abstract_inverted_index":{"The":[0,32],"probabilistic":[1],"hesitant":[2],"multiplicative":[3,77],"preference":[4,41,78],"relations":[5],"(PHMPRs)":[6],"can":[7],"model":[8,143,159],"the":[9,12,29,36,44,48,53,68,83,101,111,129,157,165],"opinions":[10],"of":[11,76,85,113,133],"decision":[13,141],"makers":[14],"for":[15,72,89,97,105,117],"pairwise":[16],"comparisons":[17],"over":[18],"alternatives":[19],"using":[20],"some":[21],"possible":[22],"values":[23,42],"from":[24],"Saaty's":[25],"1-9":[26],"scale":[27],"with":[28,43,67,144,164],"probability":[30,45],"information.":[31],"existing":[33,166],"study":[34,167],"normalized":[35],"PHMPRs":[37,73,90,118,145],"by":[38,74],"adding":[39],"additional":[40],"information":[46],"into":[47],"shorter":[49],"element":[50],"before":[51],"modifying":[52],"consistency":[54,69,87,103],"and":[55,70,91,99,119,160],"consensus.":[56],"As":[57],"a":[58,137],"supplement,":[59],"in":[60],"this":[61],"paper,":[62],"we":[63,161],"focus":[64],"on":[65],"dealing":[66],"consensus":[71,115,124,131],"means":[75],"relations.":[79],"We":[80,107],"first":[81],"present":[82],"definition":[84],"geometric":[86,102,114,130],"index":[88,104],"develop":[92],"an":[93,122,150],"automatic":[94,123],"iterative":[95],"algorithm":[96,126],"checking":[98],"improving":[100],"PHMPRs.":[106,134],"also":[108],"put":[109,147],"forward":[110],"concept":[112],"degree":[116,132],"then":[120],"devise":[121],"reaching":[125],"to":[127,155,168],"modify":[128],"After":[135],"that,":[136],"novel":[138],"complete":[139],"group":[140],"making":[142],"is":[146,153],"forward.":[148],"Finally,":[149],"illustrative":[151],"example":[152],"shown":[154],"verify":[156],"proposed":[158],"compare":[162],"it":[163],"show":[169],"its":[170],"superiority.":[171]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
