{"id":"https://openalex.org/W3088715002","doi":"https://doi.org/10.1109/tfuzz.2020.3025697","title":"Stackelberg\u2013Nash Game Approach for Constrained Robust Optimization With Fuzzy Variables","display_name":"Stackelberg\u2013Nash Game Approach for Constrained Robust Optimization With Fuzzy Variables","publication_year":2020,"publication_date":"2020-09-23","ids":{"openalex":"https://openalex.org/W3088715002","doi":"https://doi.org/10.1109/tfuzz.2020.3025697","mag":"3088715002"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2020.3025697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.3025697","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/A5101613435","display_name":"Jie Han","orcid":"https://orcid.org/0000-0002-6357-9051"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Han","raw_affiliation_strings":["Peng Cheng Laboratory, Shenzhen, China","School of Automation, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]},{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108047088","display_name":"Chunhua Yang","orcid":"https://orcid.org/0000-0003-2550-1509"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunhua Yang","raw_affiliation_strings":["Peng Cheng Laboratory, Shenzhen, China","School of Automation, Central South University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]},{"raw_affiliation_string":"School of Automation, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023255651","display_name":"Cheng\u2010Chew Lim","orcid":"https://orcid.org/0000-0002-2463-9760"},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Cheng-Chew Lim","raw_affiliation_strings":["School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, Australia","institution_ids":["https://openalex.org/I5681781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022312188","display_name":"Xiaojun Zhou","orcid":"https://orcid.org/0000-0002-6367-696X"},"institutions":[{"id":"https://openalex.org/I4210136793","display_name":"Peng Cheng Laboratory","ror":"https://ror.org/03qdqbt06","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210136793"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaojun Zhou","raw_affiliation_strings":["Peng Cheng Laboratory, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Peng Cheng Laboratory, Shenzhen, China","institution_ids":["https://openalex.org/I4210136793"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100739668","display_name":"Peng Shi","orcid":"https://orcid.org/0000-0001-8218-586X"},"institutions":[{"id":"https://openalex.org/I5681781","display_name":"The University of Adelaide","ror":"https://ror.org/00892tw58","country_code":"AU","type":"education","lineage":["https://openalex.org/I5681781"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Peng Shi","raw_affiliation_strings":["School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, Australia","institution_ids":["https://openalex.org/I5681781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101613435"],"corresponding_institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4210136793"],"apc_list":null,"apc_paid":null,"fwci":2.4232,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.9056447,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"11","first_page":"3519","last_page":"3531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9984999895095825,"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":0.9984999895095825,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9932000041007996,"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"}},{"id":"https://openalex.org/T11053","display_name":"Process Optimization and Integration","score":0.9821000099182129,"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/stackelberg-competition","display_name":"Stackelberg competition","score":0.7379826903343201},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7322739362716675},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7161260843276978},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.638290524482727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5490487217903137},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5343078374862671},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.510810375213623},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4781250059604645},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.47627848386764526},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30250072479248047},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11828586459159851},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.08532336354255676}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.7379826903343201},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7322739362716675},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7161260843276978},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.638290524482727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5490487217903137},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5343078374862671},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.510810375213623},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4781250059604645},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.47627848386764526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30250072479248047},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11828586459159851},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.08532336354255676},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tfuzz.2020.3025697","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2020.3025697","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"},{"id":"pmh:oai:eprints.vu.edu.au:46189","is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/46189/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"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":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2225165154","display_name":null,"funder_award_id":"2018CX012","funder_id":"https://openalex.org/F4320321514","funder_display_name":"Central South University"},{"id":"https://openalex.org/G6300721355","display_name":null,"funder_award_id":"61773131","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G721055481","display_name":null,"funder_award_id":"61860206014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8359329637","display_name":null,"funder_award_id":"B17048","funder_id":"https://openalex.org/F4320327912","funder_display_name":"Higher Education Discipline Innovation Project"},{"id":"https://openalex.org/G8635280832","display_name":null,"funder_award_id":"61873285","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8915259631","display_name":null,"funder_award_id":"61873251","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/F4320321514","display_name":"Central South University","ror":"https://ror.org/00f1zfq44"},{"id":"https://openalex.org/F4320327912","display_name":"Higher Education Discipline Innovation Project","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W74565447","https://openalex.org/W560737395","https://openalex.org/W1965360346","https://openalex.org/W1994507406","https://openalex.org/W2000763566","https://openalex.org/W2050925225","https://openalex.org/W2060856116","https://openalex.org/W2068073458","https://openalex.org/W2075772595","https://openalex.org/W2131471223","https://openalex.org/W2152978141","https://openalex.org/W2157791744","https://openalex.org/W2463044584","https://openalex.org/W2591155175","https://openalex.org/W2593309838","https://openalex.org/W2598951966","https://openalex.org/W2737739803","https://openalex.org/W2763424420","https://openalex.org/W2766329821","https://openalex.org/W2804425166","https://openalex.org/W2844049989","https://openalex.org/W2884870203","https://openalex.org/W2901377556","https://openalex.org/W2903851759","https://openalex.org/W2928289619","https://openalex.org/W2944360661","https://openalex.org/W2947822183","https://openalex.org/W2976076864","https://openalex.org/W2987324255","https://openalex.org/W2994071454","https://openalex.org/W4206830167"],"related_works":["https://openalex.org/W2733656312","https://openalex.org/W2976114880","https://openalex.org/W2328458106","https://openalex.org/W2605497830","https://openalex.org/W3169439878","https://openalex.org/W2062756478","https://openalex.org/W2948291551","https://openalex.org/W4312141693","https://openalex.org/W2020507817","https://openalex.org/W1536009559"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"the":[3,23,28,48,60,63,66,72,91,102,110],"problem":[4,29],"of":[5,25],"robust":[6,32,70,104],"optimization":[7,73,105],"is":[8,44,56,79,86],"considered":[9],"for":[10,90,116],"dynamical":[11],"systems":[12],"with":[13,30,39],"both":[14,31],"constraints":[15],"and":[16,34,113],"uncertainties.":[17],"Conditions":[18],"are":[19,97],"established":[20],"to":[21,27,41,58,88,99],"ensure":[22],"existence":[24],"solutions":[26],"optimality":[33],"feasibility.":[35],"The":[36],"objective":[37],"performance":[38,112],"respect":[40],"fuzzy":[42],"uncertainties":[43,61],"evaluated":[45],"based":[46,75],"on":[47,76],"expectation-entropy":[49],"model.":[50],"A":[51,81],"feasibility":[52],"robustness":[53,111],"analysis":[54],"method":[55,106],"proposed":[57,103],"handle":[59],"in":[62,69],"constraints.":[64],"Using":[65],"hierarchy":[67],"structure":[68],"design,":[71],"framework":[74],"Stackelberg\u2013Nash":[77],"game":[78],"developed.":[80],"leader\u2013followers":[82],"state":[83],"transition":[84],"algorithm":[85],"designed":[87],"search":[89,115],"equilibrium":[92],"solution.":[93,119],"Two":[94],"application":[95],"examples":[96],"given":[98],"demonstrate":[100],"that":[101],"can":[107],"accurately":[108],"evaluate":[109],"successfully":[114],"a":[117],"compromise":[118]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}