{"id":"https://openalex.org/W2144232912","doi":"https://doi.org/10.1109/tfuzz.2009.2036907","title":"Power-Geometric Operators and Their Use in Group Decision Making","display_name":"Power-Geometric Operators and Their Use in Group Decision Making","publication_year":2009,"publication_date":"2009-11-23","ids":{"openalex":"https://openalex.org/W2144232912","doi":"https://doi.org/10.1109/tfuzz.2009.2036907","mag":"2144232912"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2009.2036907","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2009.2036907","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Fuzzy Systems","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/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908"},"institutions":[{"id":"https://openalex.org/I4210163363","display_name":"PLA Army Engineering University","ror":"https://ror.org/05mgp8x93","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210163363"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zeshui Xu","raw_affiliation_strings":["Antai School of Economic and Management, Shanghai Jiaotong University, Shanghai, China","Institute of Sciences, People''s Liberation Army University of Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Antai School of Economic and Management, Shanghai Jiaotong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Institute of Sciences, People''s Liberation Army University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I4210163363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072431554","display_name":"Ronald R. Yager","orcid":"https://orcid.org/0000-0003-2938-1858"},"institutions":[{"id":"https://openalex.org/I173466955","display_name":"Iona College","ror":"https://ror.org/00m79dm66","country_code":"US","type":"education","lineage":["https://openalex.org/I173466955"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R.R. Yager","raw_affiliation_strings":["Machine Intelligence Institute, Iona College, New Rochelle, NY, USA"],"affiliations":[{"raw_affiliation_string":"Machine Intelligence Institute, Iona College, New Rochelle, NY, USA","institution_ids":["https://openalex.org/I173466955"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100437308"],"corresponding_institution_ids":["https://openalex.org/I183067930","https://openalex.org/I4210163363"],"apc_list":null,"apc_paid":null,"fwci":11.2481,"has_fulltext":false,"cited_by_count":359,"citation_normalized_percentile":{"value":0.98684481,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"18","issue":"1","first_page":"94","last_page":"105"},"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/T11223","display_name":"Maritime Ports and Logistics","score":0.913100004196167,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.771574854850769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7094857692718506},{"id":"https://openalex.org/keywords/weighted-geometric-mean","display_name":"Weighted geometric mean","score":0.6808629035949707},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.6310675740242004},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.6274883151054382},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6273654699325562},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5779334306716919},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.45335307717323303},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37565547227859497},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3607338070869446},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1406179964542389},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11433809995651245}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.771574854850769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7094857692718506},{"id":"https://openalex.org/C117656884","wikidata":"https://www.wikidata.org/wiki/Q2625569","display_name":"Weighted geometric mean","level":3,"score":0.6808629035949707},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.6310675740242004},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.6274883151054382},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6273654699325562},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5779334306716919},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.45335307717323303},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37565547227859497},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3607338070869446},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1406179964542389},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11433809995651245},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2009.2036907","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2009.2036907","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W161157074","https://openalex.org/W194786220","https://openalex.org/W342961310","https://openalex.org/W605118308","https://openalex.org/W1503448614","https://openalex.org/W1521108275","https://openalex.org/W1968642553","https://openalex.org/W1971403896","https://openalex.org/W1973104643","https://openalex.org/W1978889792","https://openalex.org/W1984880160","https://openalex.org/W1988442031","https://openalex.org/W2004513102","https://openalex.org/W2014017874","https://openalex.org/W2022373133","https://openalex.org/W2025124974","https://openalex.org/W2044770310","https://openalex.org/W2047833440","https://openalex.org/W2048305092","https://openalex.org/W2055892602","https://openalex.org/W2060907774","https://openalex.org/W2061963820","https://openalex.org/W2081331155","https://openalex.org/W2081754091","https://openalex.org/W2089336319","https://openalex.org/W2117827905","https://openalex.org/W2129521002","https://openalex.org/W2130104797","https://openalex.org/W2134812582","https://openalex.org/W2137911902","https://openalex.org/W2147595926","https://openalex.org/W2150546380","https://openalex.org/W2157339075","https://openalex.org/W2157687268","https://openalex.org/W2168867141","https://openalex.org/W2168936936","https://openalex.org/W2315749593","https://openalex.org/W2321974580","https://openalex.org/W2326315219","https://openalex.org/W2481052802","https://openalex.org/W2482048267","https://openalex.org/W4236700867","https://openalex.org/W4236702134","https://openalex.org/W4243419638"],"related_works":["https://openalex.org/W2128177177","https://openalex.org/W2002768246","https://openalex.org/W2069750915","https://openalex.org/W2288790715","https://openalex.org/W2369650867","https://openalex.org/W2096851309","https://openalex.org/W4254478543","https://openalex.org/W2027369157","https://openalex.org/W2149623705","https://openalex.org/W3151496173"],"abstract_inverted_index":{"The":[0],"power-average":[1],"(PA)":[2],"operator":[3,8,32,45,55,69,117,127],"and":[4,33,46,50,56,70,74,88,91,97,105,118,122,147,164,169],"the":[5,10,21,40,43,47,64,67,71,83,86,92,95,103,130,134,144,166,191],"power-ordered-weighted-average":[6],"(POWA)":[7],"are":[9,38,62],"two":[11],"nonlinear":[12],"weighted-average":[13],"aggregation":[14],"tools":[15],"whose":[16],"weighting":[17],"vectors":[18],"depend":[19],"on":[20,39,63,160,182],"input":[22,131],"arguments.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,101,142,188],"develop":[28,51,112,152,174],"a":[29,52,57],"power-geometric":[30],"(PG)":[31],"its":[34,119],"weighted":[35,120,145,167],"form,":[36,121],"which":[37,61],"basis":[41,65],"of":[42,66,77,136,138],"PA":[44,87],"geometric":[48,72],"mean,":[49,73],"power-ordered-geometric":[53],"(POG)":[54],"power-ordered-weighted-geometric":[58,125],"(POWG)":[59],"operator,":[60],"POWA":[68,96],"study":[75],"some":[76],"their":[78],"properties.":[79],"We":[80],"also":[81],"discuss":[82],"relationship":[84,93],"between":[85,94],"PG":[89,104,115,146],"operators":[90,107],"POWG":[98,106,148],"operators.":[99],"Then,":[100],"extend":[102],"to":[108,128,151,155,173,177,194],"uncertain":[109,114,124,183],"environments,":[110],"i.e.,":[111],"an":[113,123,153,175],"(UPG)":[116],"(UPOWG)":[126],"aggregate":[129],"arguments":[132],"taking":[133],"form":[135],"interval":[137],"numerical":[139],"values.":[140],"Furthermore,":[141],"utilize":[143,165],"operators,":[149,171],"respectively,":[150,172],"approach":[154,176],"group":[156,178],"decision":[157,179],"making":[158,180],"based":[159,181],"multiplicative":[161,184],"preference":[162,185],"relations":[163],"UPG":[168],"UPOWG":[170],"relations.":[186],"Finally,":[187],"apply":[189],"both":[190],"developed":[192],"approaches":[193],"broadband":[195],"Internet-service":[196],"selection.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":40},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":29},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":43},{"year":2018,"cited_by_count":40},{"year":2017,"cited_by_count":28},{"year":2016,"cited_by_count":25},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":15}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
