{"id":"https://openalex.org/W1985630673","doi":"https://doi.org/10.1007/s10898-008-9392-9","title":"Equivalence theorem, consistency and axiomatizations of a multi-choice value","display_name":"Equivalence theorem, consistency and axiomatizations of a multi-choice value","publication_year":2008,"publication_date":"2008-12-31","ids":{"openalex":"https://openalex.org/W1985630673","doi":"https://doi.org/10.1007/s10898-008-9392-9","mag":"1985630673"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-008-9392-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-008-9392-9","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","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/A5060738416","display_name":"Yan-An Hwang","orcid":"https://orcid.org/0000-0002-3874-9338"},"institutions":[{"id":"https://openalex.org/I33096239","display_name":"National Dong Hwa University","ror":"https://ror.org/00mng9617","country_code":"TW","type":"education","lineage":["https://openalex.org/I33096239"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yan-An Hwang","raw_affiliation_strings":["Department of Applied Mathematics, National Dong Hwa University, Hualien, 974, Taiwan, ROC","Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC 974#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Dong Hwa University, Hualien, 974, Taiwan, ROC","institution_ids":["https://openalex.org/I33096239"]},{"raw_affiliation_string":"Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, ROC 974#TAB#","institution_ids":["https://openalex.org/I33096239"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101956010","display_name":"Yu-Hsien Liao","orcid":"https://orcid.org/0000-0002-1063-1143"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yu-Hsien Liao","raw_affiliation_strings":["Department of Mathematics, Chung Jen College of Nursing, Health Science and Management, Chia Yi, 600, Taiwan, ROC","Department of Mathematics, Chung Jen College of Nursing, Health Science and Management, Chia Yi, Taiwan, ROC 600#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chung Jen College of Nursing, Health Science and Management, Chia Yi, 600, Taiwan, ROC","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Chung Jen College of Nursing, Health Science and Management, Chia Yi, Taiwan, ROC 600#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101956010"],"corresponding_institution_ids":[],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":3.0481,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92784951,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"45","issue":"4","first_page":"597","last_page":"613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.996399998664856,"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/T11031","display_name":"Game Theory and Applications","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.910431981086731},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.8214178085327148},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7503286004066467},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6446822285652161},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6294071674346924},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5967780947685242},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5574994683265686},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5320689678192139},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4236978590488434},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3687344193458557},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36832958459854126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.910431981086731},{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.8214178085327148},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7503286004066467},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6446822285652161},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6294071674346924},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5967780947685242},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5574994683265686},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5320689678192139},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4236978590488434},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3687344193458557},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36832958459854126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":2,"locations":[{"id":"doi:10.1007/s10898-008-9392-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-008-9392-9","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:45:y:2009:i:4:p:597-613","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-008-9392-9","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":"Reduced inequalities","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W289424317","https://openalex.org/W659121508","https://openalex.org/W1001287412","https://openalex.org/W1513527722","https://openalex.org/W1562353621","https://openalex.org/W1604860479","https://openalex.org/W1974905181","https://openalex.org/W1986823232","https://openalex.org/W1999299714","https://openalex.org/W2035101228","https://openalex.org/W2040217797","https://openalex.org/W2041121948","https://openalex.org/W2046693296","https://openalex.org/W2090077857","https://openalex.org/W2113726644","https://openalex.org/W2259808229","https://openalex.org/W2609964325","https://openalex.org/W3123605639"],"related_works":["https://openalex.org/W4249226508","https://openalex.org/W2380202880","https://openalex.org/W4233790924","https://openalex.org/W3126099358","https://openalex.org/W4256656994","https://openalex.org/W3123621610","https://openalex.org/W2169227624","https://openalex.org/W2008082683","https://openalex.org/W2134939199","https://openalex.org/W1894585900"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}