{"id":"https://openalex.org/W2558313990","doi":"https://doi.org/10.1142/s0217595916500470","title":"A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers","display_name":"A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers","publication_year":2016,"publication_date":"2016-11-29","ids":{"openalex":"https://openalex.org/W2558313990","doi":"https://doi.org/10.1142/s0217595916500470","mag":"2558313990"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595916500470","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5103569901","display_name":"Sanjiv Kumar","orcid":null},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"funder","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sanjiv Kumar","raw_affiliation_strings":["Department of Mathematics, Delhi University, Delhi, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Delhi University, Delhi, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110792573","display_name":"Ritika Chopra","orcid":null},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"funder","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ritika Chopra","raw_affiliation_strings":["Department of Mathematics, Delhi University, Delhi, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Delhi University, Delhi, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025991329","display_name":"Ratnesh R. Saxena","orcid":"https://orcid.org/0000-0001-9622-0814"},"institutions":[{"id":"https://openalex.org/I4210095530","display_name":"Deen Dayal Upadhyay Hospital","ror":"https://ror.org/00n3vh666","country_code":"IN","type":"healthcare","lineage":["https://openalex.org/I4210095530"]},{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"funder","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ratnesh R. Saxena","raw_affiliation_strings":["Department of Mathematics, Deen Dayal Upadhyay College, Delhi University, Delhi, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Deen Dayal Upadhyay College, Delhi University, Delhi, India","institution_ids":["https://openalex.org/I4210095530","https://openalex.org/I110166357"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103569901"],"corresponding_institution_ids":["https://openalex.org/I110166357"],"apc_list":null,"apc_paid":null,"fwci":0.274,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":7,"citation_normalized_percentile":{"value":0.81733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":83,"max":84},"biblio":{"volume":"33","issue":"06","first_page":"1650047","last_page":"1650047"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.994,"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":0.994,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9823,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9343,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.4910369},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47210494}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.64565223},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6005064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5977386},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5704956},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.4910369},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47210494},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.42177114},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.3676143},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.34089738},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29126802},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.28725284},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.27847004},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.21916774},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08551073},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595916500470","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.44,"id":"https://metadata.un.org/sdg/11"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":22,"referenced_works":["https://openalex.org/W1580809199","https://openalex.org/W1965096608","https://openalex.org/W1968201190","https://openalex.org/W1983294580","https://openalex.org/W1996599288","https://openalex.org/W2009341455","https://openalex.org/W2010742660","https://openalex.org/W2037663509","https://openalex.org/W2075358004","https://openalex.org/W2093263919","https://openalex.org/W2094815170","https://openalex.org/W2103414474","https://openalex.org/W2107527466","https://openalex.org/W2131088269","https://openalex.org/W2142647383","https://openalex.org/W2154640240","https://openalex.org/W2159383497","https://openalex.org/W2408477877","https://openalex.org/W3124736843","https://openalex.org/W4211007335","https://openalex.org/W4298258403","https://openalex.org/W4302408267"],"related_works":["https://openalex.org/W4232189424","https://openalex.org/W4211138458","https://openalex.org/W3186986613","https://openalex.org/W2766459764","https://openalex.org/W2276575217","https://openalex.org/W2215997563","https://openalex.org/W2183914310","https://openalex.org/W2073992381","https://openalex.org/W2023280083","https://openalex.org/W1990178198"],"abstract_inverted_index":{"The":[0,22,51,83],"aim":[1],"of":[2,17,44,80],"this":[3,93],"paper":[4],"is":[5,54,64,117],"to":[6,57,66,75,119],"develop":[7],"an":[8,87],"effective":[9],"method":[10,23,85,91],"for":[11],"solving":[12],"matrix":[13,40,52,97],"game":[14,41,53],"with":[15,42,99],"payoffs":[16,43],"trapezoidal":[18,104],"fuzzy":[19,35,49,59,105],"numbers":[20],"(TrFNs).":[21],"always":[24,110],"assures":[25],"that":[26],"players\u2019":[27],"gain-floor":[28],"and":[29,37],"loss-ceiling":[30],"have":[31],"a":[32,47,58],"common":[33],"TrFN-type":[34,48],"value":[36,79],"hereby":[38],"any":[39],"TrFNs":[45],"has":[46,86],"value.":[50],"first":[55],"converted":[56,65],"linear":[60],"programming":[61],"problem,":[62],"which":[63,71,107],"three":[67],"different":[68],"optimization":[69],"problems,":[70],"are":[72],"then":[73],"solved":[74],"get":[76],"the":[77,81,112,121],"optimum":[78],"game.":[82],"proposed":[84],"edge":[88],"over":[89],"other":[90],"as":[92,102],"focuses":[94],"only":[95],"on":[96],"games":[98],"payoff":[100],"element":[101],"symmetric":[103],"number,":[106],"might":[108],"not":[109],"be":[111],"case.":[113],"A":[114],"numerical":[115],"example":[116],"given":[118],"illustrate":[120],"method.":[122]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2558313990","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-04-20T14:45:47.087841","created_date":"2016-12-08"}