{"id":"https://openalex.org/W2016695251","doi":"https://doi.org/10.1016/s1571-0661(04)80720-5","title":"A Rough Set Approach to Estimating the Game Value and the Shapley Value from Data","display_name":"A Rough Set Approach to Estimating the Game Value and the Shapley Value from Data","publication_year":2003,"publication_date":"2003-03-01","ids":{"openalex":"https://openalex.org/W2016695251","doi":"https://doi.org/10.1016/s1571-0661(04)80720-5","mag":"2016695251"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80720-5","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80720-5","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80720-5","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012433970","display_name":"Lech Polkowski","orcid":"https://orcid.org/0000-0002-6990-3959"},"institutions":[{"id":"https://openalex.org/I3017851245","display_name":"Polish-Japanese Academy of Information Technology","ror":"https://ror.org/01v542j61","country_code":"PL","type":"education","lineage":["https://openalex.org/I3017851245"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Lech Polkowski","raw_affiliation_strings":["Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, Poland","institution_ids":["https://openalex.org/I3017851245"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034773726","display_name":"Boles\u0142aw Araszkiewicz","orcid":null},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Boles\u0142aw Araszkiewicz","raw_affiliation_strings":["Department of Mathematics and Computer Science, Univ. Warmia and Mazury, Olsztyn, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Univ. Warmia and Mazury, Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012433970"],"corresponding_institution_ids":["https://openalex.org/I3017851245"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.13546837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"82","issue":"4","first_page":"219","last_page":"227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9889000058174133,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9746999740600586,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.9260276556015015},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.7139374613761902},{"id":"https://openalex.org/keywords/bondareva\u2013shapley-theorem","display_name":"Bondareva\u2013Shapley theorem","score":0.6949313879013062},{"id":"https://openalex.org/keywords/cooperative-game-theory","display_name":"Cooperative game theory","score":0.6034852862358093},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5941005945205688},{"id":"https://openalex.org/keywords/example-of-a-game-without-a-value","display_name":"Example of a game without a value","score":0.5863604545593262},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5582503080368042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5449721217155457},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4910280704498291},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4636342227458954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3269036114215851},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.30808311700820923},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28619593381881714},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.27591726183891296},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08682465553283691}],"concepts":[{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.9260276556015015},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.7139374613761902},{"id":"https://openalex.org/C51074407","wikidata":"https://www.wikidata.org/wiki/Q4941364","display_name":"Bondareva\u2013Shapley theorem","level":5,"score":0.6949313879013062},{"id":"https://openalex.org/C2781416736","wikidata":"https://www.wikidata.org/wiki/Q105354050","display_name":"Cooperative game theory","level":3,"score":0.6034852862358093},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5941005945205688},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.5863604545593262},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5582503080368042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5449721217155457},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4910280704498291},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4636342227458954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3269036114215851},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.30808311700820923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28619593381881714},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.27591726183891296},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08682465553283691},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(04)80720-5","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80720-5","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80720-5","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80720-5","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W148430901","https://openalex.org/W576551513","https://openalex.org/W590021423","https://openalex.org/W1526500914","https://openalex.org/W1537705438","https://openalex.org/W1557923305","https://openalex.org/W1562353621","https://openalex.org/W1582485368","https://openalex.org/W1995088126","https://openalex.org/W2007602094","https://openalex.org/W2041660482","https://openalex.org/W2075567596","https://openalex.org/W2144846366","https://openalex.org/W2498639714","https://openalex.org/W2912748361","https://openalex.org/W2913141873","https://openalex.org/W4255833381","https://openalex.org/W6722226382","https://openalex.org/W6758800615"],"related_works":["https://openalex.org/W1998702299","https://openalex.org/W1996049950","https://openalex.org/W1501424052","https://openalex.org/W2016695251","https://openalex.org/W2054979418","https://openalex.org/W66826376","https://openalex.org/W3118090749","https://openalex.org/W4281561852","https://openalex.org/W1576817755","https://openalex.org/W3124047162"],"abstract_inverted_index":{"A":[0,30,53],"value":[1,16,50,55,61,74,125,138,143,171,200],"of":[2,18,33,49,56,80,102,112,135,144,163,172,188,201,208,211,223,228,237,259],"a":[3,7,60,65,137,145,148,186,234],"game":[4,58,146,174],"v":[5,45,62],"is":[6,64],"function":[8],"which":[9,46,193],"to":[10,123,156],"each":[11,70],"coalition":[12],"S":[13],"assigns":[14],"the":[15,22,57,73,77,81,85,100,133,152,159,166,169,173,177,198,202,206,209,226],"v(S)":[17],"this":[19,157,250],"coalition,":[20,191],"meaning":[21],"expected":[23,78],"pay\u2013off":[24],"for":[25,69],"players":[26],"in":[27,84,116,241,249],"that":[28],"coalition.":[29],"classical":[31],"approach":[32],"von":[34],"Neumann":[35],"and":[36,104,168,179,221],"Morgenstern":[37],"[6]":[38],"had":[39],"set":[40,106,161,227,239],"some":[41],"formal":[42],"requirements":[43],"on":[44,99,192,217],"contemporary":[47],"theories":[48],"adhere":[51],"to.":[52],"Shapley":[54,181,257],"with":[59],"[14]":[63],"functional":[66],"\u03a6":[67],"giving":[68,197],"player":[71,82],"p":[72,83],"\u03a6p(v)":[75],"estimating":[76,136],"pay-off":[79],"game.":[86,153],"Game":[87],"as":[88,90,118,120,139,141,254,256],"well":[89,119,140,255],"conflict":[91],"theory":[92],"have":[93,127],"been":[94,128],"given":[95],"recently":[96],"much":[97],"attention":[98],"part":[101],"rough":[103,160,238],"fuzzy":[105],"communities":[107],"[11,8,1,4,7,2].":[108],"In":[109],"particular,":[110],"problems":[111,121],"plausible":[113],"strategies":[114],"[1]":[115],"conflicts":[117],"related":[122],"Shapley's":[124,142],"[3,2]":[126],"addressed.":[129],"We":[130,154,183],"confront":[131],"here":[132],"problem":[134],"from":[147,244],"partial":[149],"data":[150],"about":[151],"apply":[155],"end":[158],"ideas":[162],"approximations,":[164],"defining":[165],"lower":[167,178],"upper":[170,180],"and,":[175],"respectively,":[176],"value.":[182],"also":[184],"define":[185],"notion":[187],"an":[189],"exact":[190,212],"both":[194],"values":[195,253,258],"coincide":[196],"true":[199],"game;":[203],"we":[204],"investigate":[205],"structure":[207],"family":[210],"sets":[213,232],"showing":[214],"its":[215],"closeness":[216],"complements,":[218],"disjoint":[219],"sums,":[220],"intersections":[222],"coalitions":[224],"covering":[225],"players.":[229],"This":[230],"work":[231],"open":[233],"new":[235],"area":[236],"applications":[240],"mining":[242],"constructs":[243],"data.":[245],"The":[246],"construct":[247],"mined":[248],"case":[251],"are":[252],"games.":[260]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}