{"id":"https://openalex.org/W3011666723","doi":"https://doi.org/10.1109/tfuzz.2020.2981006","title":"A Direct Approach to Compute Triangular Fuzzy Banzhaf Values of Cooperative Games With Coalitions\u2019 Values Represented by Triangular Fuzzy Numbers","display_name":"A Direct Approach to Compute Triangular Fuzzy Banzhaf Values of Cooperative Games With Coalitions\u2019 Values Represented by Triangular Fuzzy Numbers","publication_year":2020,"publication_date":"2020-03-17","ids":{"openalex":"https://openalex.org/W3011666723","doi":"https://doi.org/10.1109/tfuzz.2020.2981006","mag":"3011666723"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2020.2981006","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.2981006","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on 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/A5074205324","display_name":"Yin-Fang Ye","orcid":"https://orcid.org/0000-0002-4344-8089"},"institutions":[{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yin-Fang Ye","raw_affiliation_strings":["School of Business Administration, Jimei University, Xiamen, China"],"raw_orcid":"https://orcid.org/0000-0002-4344-8089","affiliations":[{"raw_affiliation_string":"School of Business Administration, Jimei University, Xiamen, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115599134","display_name":"Deng-Feng Li","orcid":null},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Deng-Feng Li","raw_affiliation_strings":["School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-1537-4315","affiliations":[{"raw_affiliation_string":"School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074205324"],"corresponding_institution_ids":["https://openalex.org/I161346416"],"apc_list":null,"apc_paid":null,"fwci":5.3875,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.95863629,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"29","issue":"6","first_page":"1567","last_page":"1575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9965000152587891,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.95169997215271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7495472431182861},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.7077340483665466},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6959127187728882},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5467792749404907},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48098719120025635},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4741634428501129},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43197375535964966},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42990541458129883},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42743104696273804},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4103376269340515},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3488598167896271},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.321099191904068},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2349100410938263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21635299921035767},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14529648423194885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09634143114089966}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7495472431182861},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.7077340483665466},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6959127187728882},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5467792749404907},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48098719120025635},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4741634428501129},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43197375535964966},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42990541458129883},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42743104696273804},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4103376269340515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3488598167896271},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.321099191904068},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2349100410938263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21635299921035767},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14529648423194885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09634143114089966},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2020.2981006","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.2981006","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1979427845","https://openalex.org/W1985318641","https://openalex.org/W1987887834","https://openalex.org/W2018339197","https://openalex.org/W2031588308","https://openalex.org/W2032412713","https://openalex.org/W2033704240","https://openalex.org/W2066089804","https://openalex.org/W2088006926","https://openalex.org/W2090854437","https://openalex.org/W2118020949","https://openalex.org/W2125273027","https://openalex.org/W2128324764","https://openalex.org/W2130544162","https://openalex.org/W2148579014","https://openalex.org/W2150225271","https://openalex.org/W2153675089","https://openalex.org/W2301869342","https://openalex.org/W2318967567","https://openalex.org/W2330022088","https://openalex.org/W2462563744","https://openalex.org/W2498639714","https://openalex.org/W2537325188","https://openalex.org/W2564732733","https://openalex.org/W2604813404","https://openalex.org/W2607670898","https://openalex.org/W2625453276","https://openalex.org/W2755020064","https://openalex.org/W2771616781","https://openalex.org/W2793000682","https://openalex.org/W2893539232","https://openalex.org/W2898831885","https://openalex.org/W3124605040","https://openalex.org/W4248321094"],"related_works":["https://openalex.org/W2015274193","https://openalex.org/W2326219880","https://openalex.org/W4380992992","https://openalex.org/W2167748116","https://openalex.org/W2035087110","https://openalex.org/W2160831542","https://openalex.org/W2894688340","https://openalex.org/W2098767154","https://openalex.org/W85217607","https://openalex.org/W3187601603"],"abstract_inverted_index":{"The":[0,149],"primary":[1],"goal":[2],"of":[3,24,49,62,91,119,142,157,176,189],"this":[4,55],"article":[5],"is":[6,85],"to":[7],"develop":[8],"a":[9,21,60,196],"direct":[10],"and":[11,102,113,116,128,136,139,184,187],"simplified":[12],"approach":[13,151,192],"for":[14,20,42],"computing":[15],"triangular":[16,32,38,51,69,121,145,158,178],"fuzzy":[17,33,39,52,70,122,146,159,179],"Banzhaf":[18,89,123,180],"values":[19,29,90,124,181],"special":[22],"class":[23],"cooperative":[25,40,65,71,77,82,94,98],"games":[26,41,66,78,95,99],"with":[27,45,67,79,96,195],"coalitions'":[28,50,144],"represented":[30],"by":[31],"numbers,":[34],"which":[35],"are":[36,100,182,193],"called":[37],"short.":[43],"Combining":[44],"the":[46,68,80,88,92,111,114,120,134,137,143,155,166,177,185,190],"\u03b2-cut":[47],"sets":[48],"values,":[53,147],"in":[54],"article,":[56],"we":[57,74],"can":[58,125,163],"obtain":[59],"series":[61],"associated":[63,76,93],"interval-valued":[64,81,97],"games.":[72,83],"Hereby,":[73],"construct":[75],"It":[84],"proven":[86,183],"that":[87],"monotonic":[101],"nondecreasing":[103],"functions":[104],"under":[105],"some":[106,173],"size":[107],"monotonicity-like":[108],"conditions.":[109],"Hence,":[110],"mean":[112],"lower":[115,138],"upper":[117,140],"limits":[118,141],"be":[126],"directly":[127],"explicitly":[129],"attained":[130],"through":[131],"using":[132],"only":[133],"mean,":[135],"respectively.":[148],"developed":[150,191],"does":[152],"not":[153],"use":[154],"subtraction":[156],"numbers":[160],"and,":[161],"hereby,":[162],"effectively":[164],"avoid":[165],"irrational":[167],"issues":[168],"resulting":[169],"from":[170],"it.":[171],"Furthermore,":[172],"important":[174],"properties":[175],"applicability":[186],"validity":[188],"illustrated":[194],"numerical":[197],"example.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}