{"id":"https://openalex.org/W7140693370","doi":"https://doi.org/10.1016/j.jfranklin.2026.108594","title":"Integral reinforcement learning for optimal multiplayer games: Interval type-2 fuzzy Markov jump systems with unknown dynamics","display_name":"Integral reinforcement learning for optimal multiplayer games: Interval type-2 fuzzy Markov jump systems with unknown dynamics","publication_year":2026,"publication_date":"2026-03-26","ids":{"openalex":"https://openalex.org/W7140693370","doi":"https://doi.org/10.1016/j.jfranklin.2026.108594"},"language":"en","primary_location":{"id":"doi:10.1016/j.jfranklin.2026.108594","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2026.108594","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","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":null,"display_name":"Yuxin Sun","orcid":"https://orcid.org/0009-0007-7322-9366"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuxin Sun","raw_affiliation_strings":["School of Engineering, Qufu Normal University, Rizhao, 276826, China"],"raw_orcid":"https://orcid.org/0009-0007-7322-9366","affiliations":[{"raw_affiliation_string":"School of Engineering, Qufu Normal University, Rizhao, 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054705892","display_name":"Wenhai Qi","orcid":"https://orcid.org/0000-0002-9065-0802"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenhai Qi","raw_affiliation_strings":["School of Engineering, Qufu Normal University, Rizhao, 276826, China"],"raw_orcid":"https://orcid.org/0000-0002-9065-0802","affiliations":[{"raw_affiliation_string":"School of Engineering, Qufu Normal University, Rizhao, 276826, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130704795","display_name":"Jinde Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, 211189, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, 211189, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130698395","display_name":"Jun Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I29739308","display_name":"Guangxi Normal University","ror":"https://ror.org/02frt9q65","country_code":"CN","type":"education","lineage":["https://openalex.org/I29739308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Cheng","raw_affiliation_strings":["College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, China","institution_ids":["https://openalex.org/I29739308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130715721","display_name":"Kaibo Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaibo Shi","raw_affiliation_strings":["School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China","institution_ids":["https://openalex.org/I4210125143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054705892"],"corresponding_institution_ids":["https://openalex.org/I202126657"],"apc_list":{"value":2700,"currency":"USD","value_usd":2700},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38514976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"363","issue":"7","first_page":"108594","last_page":"108594"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.5967000126838684,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.5967000126838684,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.30799999833106995,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.013000000268220901,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.7329999804496765},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5651999711990356},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5455999970436096},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4887000024318695},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4632999897003174},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.41040000319480896},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4090999960899353}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7329999804496765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6367999911308289},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5651999711990356},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4887000024318695},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.41040000319480896},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4090999960899353},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4032999873161316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3991999924182892},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.38670000433921814},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C188116033","wikidata":"https://www.wikidata.org/wiki/Q2664563","display_name":"Q-learning","level":3,"score":0.3398999869823456},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.3379000127315521},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.3142000138759613},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3066999912261963},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.26249998807907104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C2780049643","wikidata":"https://www.wikidata.org/wiki/Q5511139","display_name":"Fuzzy rule","level":4,"score":0.2517000138759613}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.jfranklin.2026.108594","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jfranklin.2026.108594","pdf_url":null,"source":{"id":"https://openalex.org/S183498172","display_name":"Journal of the Franklin Institute","issn_l":"0016-0032","issn":["0016-0032","1879-2693"],"is_oa":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Franklin Institute","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6976671814918518,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2096325282","display_name":null,"funder_award_id":"tsqn202408169","funder_id":"https://openalex.org/F4320326189","funder_display_name":"Taishan Scholar Project of Shandong Province"},{"id":"https://openalex.org/G5451752748","display_name":null,"funder_award_id":"62473226","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326189","display_name":"Taishan Scholar Project of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W2055300044","https://openalex.org/W2069038223","https://openalex.org/W2132778652","https://openalex.org/W3047879910","https://openalex.org/W3092473112","https://openalex.org/W3096116883","https://openalex.org/W3096838109","https://openalex.org/W3112664346","https://openalex.org/W3127008750","https://openalex.org/W3137906938","https://openalex.org/W3163723204","https://openalex.org/W3190436412","https://openalex.org/W4285505520","https://openalex.org/W4297359417","https://openalex.org/W4300863038","https://openalex.org/W4302275452","https://openalex.org/W4307776787","https://openalex.org/W4308209945","https://openalex.org/W4308616306","https://openalex.org/W4312468811","https://openalex.org/W4323833140","https://openalex.org/W4364856517","https://openalex.org/W4385287472","https://openalex.org/W4386025689","https://openalex.org/W4387886154","https://openalex.org/W4389920468","https://openalex.org/W4392303036","https://openalex.org/W4400187832","https://openalex.org/W4401607407","https://openalex.org/W4401833032","https://openalex.org/W4401879498","https://openalex.org/W4402330678","https://openalex.org/W4405022224","https://openalex.org/W4406721737","https://openalex.org/W4406728006","https://openalex.org/W4407722664","https://openalex.org/W4409057749","https://openalex.org/W4409671443","https://openalex.org/W4409683775","https://openalex.org/W4410491701"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2026-03-27T00:00:00"}