{"id":"https://openalex.org/W4286487557","doi":"https://doi.org/10.1080/01605682.2022.2096503","title":"New additive-consistency-driven methods for deriving two types of normalized utility vectors from additive reciprocal preference relations","display_name":"New additive-consistency-driven methods for deriving two types of normalized utility vectors from additive reciprocal preference relations","publication_year":2022,"publication_date":"2022-07-22","ids":{"openalex":"https://openalex.org/W4286487557","doi":"https://doi.org/10.1080/01605682.2022.2096503"},"language":"en","primary_location":{"id":"doi:10.1080/01605682.2022.2096503","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01605682.2022.2096503","pdf_url":null,"source":{"id":"https://openalex.org/S169988927","display_name":"Journal of the Operational Research Society","issn_l":"0160-5682","issn":["0160-5682","1476-9360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319703","host_organization_name":"Palgrave Macmillan","host_organization_lineage":["https://openalex.org/P4310319703","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Palgrave Macmillan","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Operational Research Society","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/A5042741035","display_name":"Xiayu Tong","orcid":"https://orcid.org/0000-0002-9336-5740"},"institutions":[{"id":"https://openalex.org/I90727586","display_name":"Zhejiang University of Finance and Economics","ror":"https://ror.org/055vj5234","country_code":"CN","type":"education","lineage":["https://openalex.org/I90727586"]},{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiayu Tong","raw_affiliation_strings":["College of Entrepreneurship, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, China","School of Education Science, Nanjing Normal University, Nanjing, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Entrepreneurship, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, China","institution_ids":["https://openalex.org/I90727586"]},{"raw_affiliation_string":"School of Education Science, Nanjing Normal University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069928262","display_name":"Zhou-Jing Wang","orcid":"https://orcid.org/0000-0001-5778-5855"},"institutions":[{"id":"https://openalex.org/I90727586","display_name":"Zhejiang University of Finance and Economics","ror":"https://ror.org/055vj5234","country_code":"CN","type":"education","lineage":["https://openalex.org/I90727586"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhou-Jing Wang","raw_affiliation_strings":["School of Information, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, China","institution_ids":["https://openalex.org/I90727586"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069928262"],"corresponding_institution_ids":["https://openalex.org/I90727586"],"apc_list":null,"apc_paid":null,"fwci":0.8167,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74786013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"74","issue":"6","first_page":"1475","last_page":"1494"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.965499997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.8310079574584961},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.6798684000968933},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5932945013046265},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.5913609862327576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5411393642425537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5264129042625427},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5156704187393188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43327391147613525},{"id":"https://openalex.org/keywords/additive-model","display_name":"Additive model","score":0.43156898021698},{"id":"https://openalex.org/keywords/weight","display_name":"Weight","score":0.42302900552749634},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.41394996643066406},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3521308898925781},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23752433061599731},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12165546417236328}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.8310079574584961},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6798684000968933},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5932945013046265},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5913609862327576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5411393642425537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5264129042625427},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5156704187393188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43327391147613525},{"id":"https://openalex.org/C203223496","wikidata":"https://www.wikidata.org/wiki/Q4681344","display_name":"Additive model","level":2,"score":0.43156898021698},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.42302900552749634},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.41394996643066406},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3521308898925781},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23752433061599731},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12165546417236328},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/01605682.2022.2096503","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01605682.2022.2096503","pdf_url":null,"source":{"id":"https://openalex.org/S169988927","display_name":"Journal of the Operational Research Society","issn_l":"0160-5682","issn":["0160-5682","1476-9360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319703","host_organization_name":"Palgrave Macmillan","host_organization_lineage":["https://openalex.org/P4310319703","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Palgrave Macmillan","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Operational Research Society","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tjorxx:v:74:y:2023:i:6:p:1475-1494","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/01605682.2022.2096503","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":0.7300000190734863,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G4733716512","display_name":null,"funder_award_id":"72171209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6597671164","display_name":"\u6a21\u7cca\u5224\u65ad\u4fe1\u606f\u4e0d\u5b8c\u5168\u4e0b\u63a7\u5236\u4e0d\u786e\u5b9a\u7a0b\u5ea6\u7684\u7fa4\u4f53\u51b3\u7b56\u6a21\u578b\u7814\u7a76","funder_award_id":"71671160","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":42,"referenced_works":["https://openalex.org/W1458841637","https://openalex.org/W1871214897","https://openalex.org/W1968027322","https://openalex.org/W1986873987","https://openalex.org/W1995906594","https://openalex.org/W1999943538","https://openalex.org/W2021767647","https://openalex.org/W2028881626","https://openalex.org/W2029606308","https://openalex.org/W2031499317","https://openalex.org/W2055892602","https://openalex.org/W2058350496","https://openalex.org/W2069403107","https://openalex.org/W2070270987","https://openalex.org/W2071460834","https://openalex.org/W2075523192","https://openalex.org/W2089336319","https://openalex.org/W2090611847","https://openalex.org/W2137911902","https://openalex.org/W2558629977","https://openalex.org/W2577307581","https://openalex.org/W2597824701","https://openalex.org/W2618394139","https://openalex.org/W2772240868","https://openalex.org/W2801348231","https://openalex.org/W2900202456","https://openalex.org/W2903709878","https://openalex.org/W2925827085","https://openalex.org/W2944129526","https://openalex.org/W2965182377","https://openalex.org/W2994728236","https://openalex.org/W2998172538","https://openalex.org/W3004561815","https://openalex.org/W3021183375","https://openalex.org/W3025601253","https://openalex.org/W3030129408","https://openalex.org/W3033417084","https://openalex.org/W3047184952","https://openalex.org/W3096359317","https://openalex.org/W3106697739","https://openalex.org/W3137607766","https://openalex.org/W3186215453"],"related_works":["https://openalex.org/W2391753177","https://openalex.org/W2996284460","https://openalex.org/W2128971439","https://openalex.org/W2379697517","https://openalex.org/W2033375693","https://openalex.org/W2005614587","https://openalex.org/W3101117982","https://openalex.org/W2350145891","https://openalex.org/W1807905406","https://openalex.org/W3089872615"],"abstract_inverted_index":{"In":[0],"multi-criteria":[1,165],"decision":[2,166],"making,":[3],"importance":[4,58],"weights":[5],"of":[6,23,61,104,130,155,191],"criteria":[7],"are":[8,77,97,117,123,148,183],"usually":[9],"derived":[10],"from":[11,85,135],"pairwise":[12,35],"comparisons":[13,36],"and":[14,74,91,119,144,175,189],"requested":[15],"for":[16],"adding":[17],"up":[18],"to":[19,52,79,99,125,150,162,185],"one.":[20],"The":[21],"framework":[22,65],"additive":[24,139,153],"reciprocal":[25],"preference":[26],"relations":[27],"(ARPRs)":[28],"is":[29,66,142,160],"a":[30,54],"commonly":[31],"used":[32],"tool":[33],"representing":[34],"under":[37,68],"the":[38,101,127,187,192],"unit":[39],"interval":[40],"scale.":[41],"This":[42],"paper":[43],"illustrates":[44],"that":[45],"existing":[46],"additive-consistency-driven":[47],"utility":[48,106,133],"derivation":[49],"methods":[50,76],"fail":[51],"acquire":[53],"satisfactory":[55],"additively":[56,81,92,111],"normalized":[57,93,105,131],"weight":[59],"vector":[60],"criteria.":[62],"A":[63,137,157],"normalization":[64,89],"introduced":[67],"an":[69,110,176],"Abelian":[70],"linearly":[71],"ordered":[72],"group":[73],"new":[75,88],"proposed":[78],"generate":[80],"consistent":[82,112],"ARPRs":[83],"respectively":[84],"vectors":[86,107,134],"satisfying":[87],"conditions":[90],"vectors.":[94],"Two":[95,169],"formulas":[96],"devised":[98],"obtain":[100],"two":[102,128],"types":[103,129],"associated":[108],"with":[109,164,172],"ARPR.":[113],"Three":[114],"optimization":[115],"models":[116],"built":[118],"their":[120],"analytical":[121],"solutions":[122],"found":[124],"derive":[126],"optimal":[132],"ARPRs.":[136,156],"geometrically":[138],"consistency":[140,154],"index":[141],"presented":[143,193],"its":[145],"approximated":[146],"thresholds":[147],"suggested":[149],"check":[151],"acceptably":[152],"stepwise":[158],"procedure":[159],"developed":[161],"deal":[163],"making":[167],"problems.":[168],"numerical":[170],"illustrations":[171],"comparative":[173],"analysis":[174],"international":[177],"exchange":[178],"postgraduate":[179],"student":[180],"selection":[181],"problem":[182],"offered":[184],"demonstrate":[186],"performance":[188],"practicality":[190],"models.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
