{"id":"https://openalex.org/W4225614998","doi":"https://doi.org/10.1007/s10479-022-04682-8","title":"Evaluating scales for pairwise comparisons","display_name":"Evaluating scales for pairwise comparisons","publication_year":2022,"publication_date":"2022-04-07","ids":{"openalex":"https://openalex.org/W4225614998","doi":"https://doi.org/10.1007/s10479-022-04682-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-022-04682-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-022-04682-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-022-04682-8.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10479-022-04682-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004123924","display_name":"Bice Cavallo","orcid":"https://orcid.org/0000-0002-5102-3232"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Bice Cavallo","raw_affiliation_strings":["Department of Architecture, University of Naples Federico II, Via Toledo 402, 80134, Naples, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5102-3232","affiliations":[{"raw_affiliation_string":"Department of Architecture, University of Naples Federico II, Via Toledo 402, 80134, Naples, Italy","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001351762","display_name":"Alessio Ishizaka","orcid":"https://orcid.org/0000-0002-2531-292X"},"institutions":[{"id":"https://openalex.org/I1289910757","display_name":"NEOMA Business School","ror":"https://ror.org/01g1pe685","country_code":"FR","type":"education","lineage":["https://openalex.org/I1289910757"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alessio Ishizaka","raw_affiliation_strings":["Information Systems, Supply Chain and Decision making Department, NEOMA Business School, 1 rue du Mar\u00e9chal Juin - BP 215, 76130, Mont-Saint-Aignan Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Systems, Supply Chain and Decision making Department, NEOMA Business School, 1 rue du Mar\u00e9chal Juin - BP 215, 76130, Mont-Saint-Aignan Cedex, France","institution_ids":["https://openalex.org/I1289910757"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004123924"],"corresponding_institution_ids":["https://openalex.org/I71267560"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.0419,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91575174,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"325","issue":"2","first_page":"951","last_page":"965"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997000098228455,"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":0.9997000098228455,"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/T12945","display_name":"Quality Function Deployment in Product Design","score":0.9394000172615051,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.9160264730453491},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6999092102050781},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6627320647239685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6112575531005859},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5344701409339905},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5328583717346191},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43261975049972534},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.41706767678260803},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3360656499862671},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30223560333251953},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2766149640083313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23179078102111816}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.9160264730453491},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6999092102050781},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6627320647239685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6112575531005859},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5344701409339905},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5328583717346191},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43261975049972534},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.41706767678260803},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3360656499862671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30223560333251953},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2766149640083313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23179078102111816},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10479-022-04682-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-022-04682-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-022-04682-8.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:annopr:v:325:y:2023:i:2:d:10.1007_s10479-022-04682-8","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10479-022-04682-8","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":{"id":"doi:10.1007/s10479-022-04682-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-022-04682-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10479-022-04682-8.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7599999904632568,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225614998.pdf","grobid_xml":"https://content.openalex.org/works/W4225614998.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W5086244","https://openalex.org/W1923138770","https://openalex.org/W1968499996","https://openalex.org/W1984126224","https://openalex.org/W2000688897","https://openalex.org/W2005208256","https://openalex.org/W2006218358","https://openalex.org/W2011499868","https://openalex.org/W2013142182","https://openalex.org/W2018220515","https://openalex.org/W2020407132","https://openalex.org/W2025932902","https://openalex.org/W2033401964","https://openalex.org/W2033442452","https://openalex.org/W2035716459","https://openalex.org/W2035756317","https://openalex.org/W2040279732","https://openalex.org/W2041826373","https://openalex.org/W2051792888","https://openalex.org/W2061196779","https://openalex.org/W2086326887","https://openalex.org/W2089336319","https://openalex.org/W2111719258","https://openalex.org/W2159322663","https://openalex.org/W2171237878","https://openalex.org/W2328864148","https://openalex.org/W2529063761","https://openalex.org/W2541151991","https://openalex.org/W2557168758","https://openalex.org/W2564049104","https://openalex.org/W2618394139","https://openalex.org/W2783981835","https://openalex.org/W2789182217","https://openalex.org/W2801348231","https://openalex.org/W2885977168","https://openalex.org/W2948954594","https://openalex.org/W2955436445","https://openalex.org/W3037052089","https://openalex.org/W3040291074","https://openalex.org/W3096009669","https://openalex.org/W3098948151","https://openalex.org/W3102581922","https://openalex.org/W3171049164","https://openalex.org/W4231777370","https://openalex.org/W4233237296","https://openalex.org/W6751054543"],"related_works":["https://openalex.org/W3033828522","https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W2010725720","https://openalex.org/W4310066305","https://openalex.org/W4224009465","https://openalex.org/W4286629047","https://openalex.org/W4306321456","https://openalex.org/W4285260836","https://openalex.org/W3046775127"],"abstract_inverted_index":{"Abstract":[0],"Pairwise":[1],"comparisons":[2,110],"have":[3,33],"been":[4,15,34],"a":[5,42,113],"long-standing":[6],"technique":[7],"for":[8,82,120],"comparing":[9],"alternatives/criteria":[10],"and":[11,112],"their":[12],"role":[13],"has":[14],"pivotal":[16],"in":[17],"the":[18,38,63,67,76,90,95,101,122],"development":[19],"of":[20,60,66,78,84,108],"modern":[21],"decision-making":[22],"methods.":[23],"The":[24,71],"evaluation":[25,40,80],"is":[26,118],"very":[27],"often":[28],"done":[29],"linguistically.":[30],"Several":[31],"scales":[32,81],"proposed":[35],"to":[36,52,74],"translate":[37],"linguistic":[39],"into":[41],"quantitative":[43],"evaluation.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48],"perform":[49],"an":[50],"experiment":[51,72],"investigate,":[53],"under":[54],"our":[55],"methodological":[56],"choices,":[57],"which":[58],"type":[59],"scale":[61,93],"provides":[62,94],"best":[64,96],"matching":[65,97,123],"decision-maker\u2019s":[68],"verbal":[69,98],"representation.":[70],"aims":[73],"evaluate":[75],"suitability":[77],"eight":[79],"problems":[83],"different":[85],"sizes.":[86],"We":[87],"find":[88],"that":[89],"inverse":[91],"linear":[92],"representation":[99],"whenever":[100],"objective":[102],"data":[103],"are":[104],"measured":[105],"by":[106],"means":[107],"pairwise":[109],"matrices":[111,117],"suitable":[114],"distance":[115],"between":[116],"applied":[119],"computing":[121],"error.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}