{"id":"https://openalex.org/W2122952453","doi":"https://doi.org/10.3233/ifs-2012-0611","title":"The Shapley function for fuzzy games with fuzzy characteristic functions","display_name":"The Shapley function for fuzzy games with fuzzy characteristic functions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2122952453","doi":"https://doi.org/10.3233/ifs-2012-0611","mag":"2122952453"},"language":"en","primary_location":{"id":"doi:10.3233/ifs-2012-0611","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-2012-0611","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; 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/A5101605116","display_name":"Fanyong Meng","orcid":"https://orcid.org/0000-0001-9636-3479"},"institutions":[{"id":"https://openalex.org/I44468530","display_name":"Qingdao University of Technology","ror":"https://ror.org/01qzc0f54","country_code":"CN","type":"education","lineage":["https://openalex.org/I44468530"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fanyong Meng","raw_affiliation_strings":["School of Management, Qingdao Technological University, Qingdao, China","[School of Management, Qingdao Technological University, Qingdao, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Qingdao Technological University, Qingdao, China","institution_ids":["https://openalex.org/I44468530"]},{"raw_affiliation_string":"[School of Management, Qingdao Technological University, Qingdao, China]","institution_ids":["https://openalex.org/I44468530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023414425","display_name":"Jinxian Zhao","orcid":"https://orcid.org/0009-0003-9642-6419"},"institutions":[{"id":"https://openalex.org/I44468530","display_name":"Qingdao University of Technology","ror":"https://ror.org/01qzc0f54","country_code":"CN","type":"education","lineage":["https://openalex.org/I44468530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinxian Zhao","raw_affiliation_strings":["School of Management, Qingdao Technological University, Qingdao, China","[School of Management, Qingdao Technological University, Qingdao, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Qingdao Technological University, Qingdao, China","institution_ids":["https://openalex.org/I44468530"]},{"raw_affiliation_string":"[School of Management, Qingdao Technological University, Qingdao, China]","institution_ids":["https://openalex.org/I44468530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100381911","display_name":"Qiang Zhang","orcid":"https://orcid.org/0000-0002-3929-1541"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiang Zhang","raw_affiliation_strings":["School of Management and Economics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management and Economics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101605116"],"corresponding_institution_ids":["https://openalex.org/I44468530"],"apc_list":null,"apc_paid":null,"fwci":1.5749,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85468942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"25","issue":"1","first_page":"23","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9980999827384949,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.98580002784729,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.671870768070221},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.5162953734397888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4624811112880707},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4294053018093109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3939051628112793},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.29924213886260986},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.21913444995880127},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18396583199501038}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.671870768070221},{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.5162953734397888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4624811112880707},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4294053018093109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3939051628112793},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.29924213886260986},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.21913444995880127},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18396583199501038},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/ifs-2012-0611","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-2012-0611","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"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":24,"referenced_works":["https://openalex.org/W18266011","https://openalex.org/W1985318641","https://openalex.org/W1991138088","https://openalex.org/W1995088126","https://openalex.org/W1995891097","https://openalex.org/W1996603728","https://openalex.org/W2006469274","https://openalex.org/W2008630501","https://openalex.org/W2011938136","https://openalex.org/W2013594001","https://openalex.org/W2035696476","https://openalex.org/W2041614165","https://openalex.org/W2045328424","https://openalex.org/W2055693373","https://openalex.org/W2080671496","https://openalex.org/W2089048646","https://openalex.org/W2092766310","https://openalex.org/W2093715448","https://openalex.org/W2113720027","https://openalex.org/W2125273027","https://openalex.org/W2157041604","https://openalex.org/W2162446004","https://openalex.org/W2167267552","https://openalex.org/W2598771954"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4249226508","https://openalex.org/W2380202880","https://openalex.org/W4233790924","https://openalex.org/W3126099358","https://openalex.org/W4256656994","https://openalex.org/W1979597421","https://openalex.org/W3123621610","https://openalex.org/W2169227624"],"abstract_inverted_index":{"In":[0],"this":[1,62],"paper,":[2],"we":[3,44,74,86],"research":[4,75,87],"fuzzy":[5,8,26,34,50,53,65,70,79,82,92,95,107],"games":[6,51,80,93,108],"with":[7,52,81,94,109],"characteristic":[9,54,83,96],"functions,":[10,55,97],"where":[11],"the":[12,30,37,41,58,68],"player":[13],"participation":[14],"levels":[15],"are":[16,25],"real":[17],"numbers":[18,35],"in":[19],"[0,":[20],"1],":[21],"and":[22,36,56],"their":[23],"payoffs":[24],"numbers.":[27],"Based":[28],"on":[29],"Hukuhara":[31],"difference":[32],"between":[33],"calculating":[38],"formula":[39],"of":[40,49,64,78,91,106],"Shapley":[42,59],"function,":[43],"discuss":[45],"a":[46,88,114],"general":[47],"form":[48],"study":[57],"function":[60],"for":[61],"kind":[63,90],"games.":[66],"When":[67],"given":[69],"game":[71],"is":[72,99,117],"convex,":[73],"some":[76],"properties":[77],"functions.":[84],"Furthermore,":[85],"special":[89],"which":[98],"can":[100],"be":[101],"seen":[102],"as":[103],"an":[104],"extension":[105,111],"multilinear":[110],"form.":[112],"Finally,":[113],"numerical":[115],"example":[116],"given.":[118]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
