{"id":"https://openalex.org/W4297238798","doi":"https://doi.org/10.1080/00207721.2022.2122903","title":"Saddle-point equilibrium for Hurwicz model considering zero-sum differential game of uncertain dynamical systems with jump","display_name":"Saddle-point equilibrium for Hurwicz model considering zero-sum differential game of uncertain dynamical systems with jump","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W4297238798","doi":"https://doi.org/10.1080/00207721.2022.2122903"},"language":"en","primary_location":{"id":"doi:10.1080/00207721.2022.2122903","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2022.2122903","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5009441423","display_name":"Xibao Li","orcid":"https://orcid.org/0000-0002-0101-5613"},"institutions":[{"id":"https://openalex.org/I63371133","display_name":"Chongqing Jiaotong University","ror":"https://ror.org/01t001k65","country_code":"CN","type":"education","lineage":["https://openalex.org/I63371133"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xi Li","raw_affiliation_strings":["Chongqing Jiaotong University","School of Economics and Management, Chongqing Jiaotong University, Chongqing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Chongqing Jiaotong University","institution_ids":["https://openalex.org/I63371133"]},{"raw_affiliation_string":"School of Economics and Management, Chongqing Jiaotong University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I63371133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047077749","display_name":"Qiankun Song","orcid":"https://orcid.org/0000-0002-7228-9371"},"institutions":[{"id":"https://openalex.org/I63371133","display_name":"Chongqing Jiaotong University","ror":"https://ror.org/01t001k65","country_code":"CN","type":"education","lineage":["https://openalex.org/I63371133"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiankun Song","raw_affiliation_strings":["Chongqing Jiaotong University","Department of Mathematics, Chongqing Jiaotong University, Chongqing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Chongqing Jiaotong University","institution_ids":["https://openalex.org/I63371133"]},{"raw_affiliation_string":"Department of Mathematics, Chongqing Jiaotong University, Chongqing, People's Republic of China","institution_ids":["https://openalex.org/I63371133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101564220","display_name":"Yurong Liu","orcid":"https://orcid.org/0000-0001-8035-288X"},"institutions":[{"id":"https://openalex.org/I4210157719","display_name":"Yancheng Institute of Technology","ror":"https://ror.org/04y8njc86","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210157719"]},{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yurong Liu","raw_affiliation_strings":["Yancheng Institute of Technology","Yangzhou University","School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, People's Republic of China","Department of Mathematics, Yangzhou University, Yangzhou, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Yancheng Institute of Technology","institution_ids":["https://openalex.org/I4210157719"]},{"raw_affiliation_string":"Yangzhou University","institution_ids":["https://openalex.org/I78978612"]},{"raw_affiliation_string":"School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, People's Republic of China","institution_ids":["https://openalex.org/I4210157719"]},{"raw_affiliation_string":"Department of Mathematics, Yangzhou University, Yangzhou, People's Republic of China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080263475","display_name":"Fuad E. Alsaadi","orcid":"https://orcid.org/0000-0001-6420-3948"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fuad E. Alsaadi","raw_affiliation_strings":["King Abdulaziz University","Communication Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"King Abdulaziz University","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Communication Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009441423"],"corresponding_institution_ids":["https://openalex.org/I63371133"],"apc_list":null,"apc_paid":null,"fwci":3.4044,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.93768466,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"54","issue":"2","first_page":"357","last_page":"370"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9814000129699707,"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/saddle-point","display_name":"Saddle point","score":0.7586538791656494},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.7293940186500549},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.6917334794998169},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.6466480493545532},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6313543915748596},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.6280708312988281},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6192232966423035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5948112607002258},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5393760800361633},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4932824969291687},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.48629626631736755},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4621162712574005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4530600309371948},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.41256436705589294},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.408974826335907},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3810204863548279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31780946254730225},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.28737589716911316},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2736686170101166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2362649142742157},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2181609570980072},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1927100419998169},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08346226811408997},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08269423246383667}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7586538791656494},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.7293940186500549},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.6917334794998169},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.6466480493545532},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6313543915748596},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6280708312988281},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6192232966423035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5948112607002258},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5393760800361633},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4932824969291687},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.48629626631736755},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4621162712574005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4530600309371948},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.41256436705589294},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.408974826335907},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3810204863548279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31780946254730225},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.28737589716911316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2736686170101166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2362649142742157},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2181609570980072},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1927100419998169},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08346226811408997},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08269423246383667},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207721.2022.2122903","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207721.2022.2122903","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tsysxx:v:54:y:2023:i:2:p:357-370","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207721.2022.2122903","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1964041205","https://openalex.org/W1990177676","https://openalex.org/W2274279545","https://openalex.org/W2783532318","https://openalex.org/W2808373972","https://openalex.org/W2998316972","https://openalex.org/W2999067740","https://openalex.org/W3014560780","https://openalex.org/W3041576967","https://openalex.org/W3044378270","https://openalex.org/W3085603931","https://openalex.org/W3085763374","https://openalex.org/W3086511271","https://openalex.org/W3087851472","https://openalex.org/W3088439536","https://openalex.org/W3089122089","https://openalex.org/W3089504774","https://openalex.org/W3091128867","https://openalex.org/W3114336879","https://openalex.org/W3114587029","https://openalex.org/W3114688962","https://openalex.org/W3129303861","https://openalex.org/W3133841657","https://openalex.org/W3138096935","https://openalex.org/W3161167804","https://openalex.org/W3161198229","https://openalex.org/W3163171063","https://openalex.org/W3164746976","https://openalex.org/W3178096653","https://openalex.org/W3178291416","https://openalex.org/W3189396819","https://openalex.org/W3191620319","https://openalex.org/W3196831667","https://openalex.org/W3197787153","https://openalex.org/W3204741771","https://openalex.org/W3205058525","https://openalex.org/W3208490979","https://openalex.org/W3208501119","https://openalex.org/W3215650268","https://openalex.org/W3217296915","https://openalex.org/W4205859350","https://openalex.org/W4206730309","https://openalex.org/W4210242604","https://openalex.org/W4221122833","https://openalex.org/W4226250341","https://openalex.org/W4231397353","https://openalex.org/W4236577982"],"related_works":["https://openalex.org/W2077432297","https://openalex.org/W2783532318","https://openalex.org/W2793678088","https://openalex.org/W3173112975","https://openalex.org/W2078184820","https://openalex.org/W2161697746","https://openalex.org/W2800356679","https://openalex.org/W1987479130","https://openalex.org/W2964933021","https://openalex.org/W1986241611"],"abstract_inverted_index":{"As":[0],"an":[1,37],"effective":[2],"vehicle,":[3],"uncertainty":[4,14],"theory":[5],"is":[6,27,34,62,78,91],"applicable":[7],"for":[8,54],"handling":[9],"subjective":[10],"indeterminacy.":[11],"Based":[12],"on":[13],"theory,":[15],"the":[16,20,31,43,56,59,66,74],"Hurwicz":[17],"model":[18],"of":[19,58],"zero-sum":[21],"uncertain":[22,38,49],"differential":[23,39],"game":[24,61,67],"with":[25,68],"jump":[26],"formulated,":[28],"in":[29],"which":[30],"dynamic":[32,71],"system":[33,72],"portrayed":[35],"by":[36],"equation":[40,53],"satisfying":[41],"both":[42],"canonical":[44],"Liu":[45],"process":[46],"and":[47,73],"V-jump":[48],"process.":[50],"An":[51],"equilibrium":[52],"solving":[55],"saddle-point":[57],"above":[60],"proposed.":[63],"In":[64],"addition,":[65],"a":[69,83],"linear":[70],"quadratic":[75],"objective":[76],"function":[77],"further":[79],"analysed.":[80],"At":[81],"last,":[82],"resource":[84],"extraction":[85],"problem":[86],"using":[87],"our":[88],"theoretical":[89],"results":[90],"described.":[92]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3}],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}