{"id":"https://openalex.org/W2317668128","doi":"https://doi.org/10.1080/03081079.2015.1086579","title":"Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application","display_name":"Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2317668128","doi":"https://doi.org/10.1080/03081079.2015.1086579","mag":"2317668128"},"language":"en","primary_location":{"id":"doi:10.1080/03081079.2015.1086579","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2015.1086579","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"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 General 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/A5060783466","display_name":"Hua Ke","orcid":"https://orcid.org/0000-0001-7206-1994"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Ke","raw_affiliation_strings":["School of Economics and Management, Tongji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068898095","display_name":"Huang Hu","orcid":"https://orcid.org/0000-0003-4717-2400"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hu Huang","raw_affiliation_strings":["School of Economics and Management, Tongji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029746376","display_name":"Dan A. Ralescu","orcid":"https://orcid.org/0000-0002-8920-3933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dan A. Ralescu","raw_affiliation_strings":["Department of Mathematical SciencesUniversity of Cincinnati, Cincinnati, OH, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical SciencesUniversity of Cincinnati, Cincinnati, OH, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100759346","display_name":"Lei Wang","orcid":"https://orcid.org/0000-0002-2387-8030"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Wang","raw_affiliation_strings":["School of Economics and Management, Tongji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068898095"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":2.9701,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91144729,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"45","issue":"3","first_page":"336","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9970999956130981,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9939000010490417,"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":0.9934999942779541,"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/computer-science","display_name":"Computer science","score":0.689932107925415},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.6381345987319946},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5801183581352234},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5242443680763245},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.5077236890792847},{"id":"https://openalex.org/keywords/supply-chain","display_name":"Supply chain","score":0.45812639594078064},{"id":"https://openalex.org/keywords/optimal-decision","display_name":"Optimal decision","score":0.4381258487701416},{"id":"https://openalex.org/keywords/decision-model","display_name":"Decision model","score":0.4290001690387726},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.42605364322662354},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.41611596941947937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2945778965950012},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2745108902454376},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.24776571989059448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22635513544082642},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17138588428497314},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.143793523311615}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.689932107925415},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6381345987319946},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5801183581352234},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5242443680763245},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.5077236890792847},{"id":"https://openalex.org/C108713360","wikidata":"https://www.wikidata.org/wiki/Q1824206","display_name":"Supply chain","level":2,"score":0.45812639594078064},{"id":"https://openalex.org/C150325174","wikidata":"https://www.wikidata.org/wiki/Q4335500","display_name":"Optimal decision","level":3,"score":0.4381258487701416},{"id":"https://openalex.org/C59594135","wikidata":"https://www.wikidata.org/wiki/Q5249242","display_name":"Decision model","level":2,"score":0.4290001690387726},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42605364322662354},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.41611596941947937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2945778965950012},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2745108902454376},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.24776571989059448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22635513544082642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17138588428497314},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.143793523311615},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03081079.2015.1086579","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2015.1086579","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"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 General Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1101679651","display_name":null,"funder_award_id":"71371141","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6093197355","display_name":"\u968f\u673a\u4e0e\u6a21\u7cca\u6df7\u5408\u73af\u5883\u4e0b\u7684\u5de5\u7a0b\u8fdb\u5ea6\u4f18\u5316\u7406\u8bba\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"71001080","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W798021849","https://openalex.org/W1484068505","https://openalex.org/W1505119482","https://openalex.org/W1588628884","https://openalex.org/W1875148622","https://openalex.org/W1964335281","https://openalex.org/W1964765773","https://openalex.org/W1966061878","https://openalex.org/W1970976252","https://openalex.org/W1974379101","https://openalex.org/W1974952991","https://openalex.org/W1975320652","https://openalex.org/W1990676004","https://openalex.org/W1992590811","https://openalex.org/W2005480674","https://openalex.org/W2007510179","https://openalex.org/W2009567498","https://openalex.org/W2012724591","https://openalex.org/W2018957554","https://openalex.org/W2024812800","https://openalex.org/W2025844219","https://openalex.org/W2031264011","https://openalex.org/W2032892248","https://openalex.org/W2041413069","https://openalex.org/W2044605166","https://openalex.org/W2049230000","https://openalex.org/W2049606892","https://openalex.org/W2062626207","https://openalex.org/W2068447057","https://openalex.org/W2079157103","https://openalex.org/W2080339050","https://openalex.org/W2095818975","https://openalex.org/W2103496339","https://openalex.org/W2124659975","https://openalex.org/W2125147066","https://openalex.org/W2128530362","https://openalex.org/W2139427936","https://openalex.org/W2159480638","https://openalex.org/W2388003275","https://openalex.org/W2543580944","https://openalex.org/W3125672793","https://openalex.org/W3143440137","https://openalex.org/W3143971390","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W1988507758","https://openalex.org/W3148242583","https://openalex.org/W2013038594","https://openalex.org/W1994921083","https://openalex.org/W2108630901","https://openalex.org/W2783384756","https://openalex.org/W575123795","https://openalex.org/W2330339184","https://openalex.org/W1510303596","https://openalex.org/W2810700601"],"abstract_inverted_index":{"In":[0,127],"centralized":[1],"decision":[2,20,42,45,117],"problems,":[3],"it":[4],"is":[5,22,28,151],"not":[6],"complicated":[7],"for":[8],"decision-makers":[9,51,67],"to":[10,33,113,129],"make":[11],"modelling":[12,86],"technique":[13],"selections":[14],"under":[15],"uncertainty.":[16],"When":[17],"a":[18,73,115,120,133],"decentralized":[19,69,121],"problem":[21,118],"considered,":[23],"however,":[24],"choosing":[25],"appropriate":[26],"models":[27,82,97,112,160],"no":[29],"longer":[30],"easy":[31],"due":[32],"the":[34,38,62,66,109,156],"difficulty":[35],"in":[36,68,88,103,119],"estimating":[37],"other":[39],"decision-makers\u2019":[40],"inconclusive":[41],"criteria.":[43],"These":[44],"criteria":[46],"may":[47,99],"vary":[48],"with":[49,84,124],"different":[50,85,89],"because":[52],"of":[53,76,95,158],"their":[54],"special":[55],"risk":[56],"tolerances":[57],"and":[58,142],"management":[59],"requirements.":[60],"Considering":[61],"general":[63,74],"differences":[64],"among":[65],"systems,":[70],"we":[71,92,107],"propose":[72],"framework":[75],"fuzzy":[77,125,138],"bilevel":[78],"programming":[79],"including":[80],"hybrid":[81,134],"(integrated":[83],"methods":[87],"levels).":[90],"Specially,":[91],"discuss":[93],"two":[94,111],"these":[96,131,159],"which":[98],"have":[100],"wide":[101],"applications":[102,157],"many":[104],"fields.":[105],"Furthermore,":[106],"apply":[108],"proposed":[110],"formulate":[114],"pricing":[116],"supply":[122],"chain":[123],"coefficients.":[126],"order":[128],"solve":[130],"models,":[132],"intelligent":[135],"algorithm":[136],"integrating":[137],"simulation,":[139],"neural":[140],"network":[141],"particle":[143],"swarm":[144],"optimization":[145],"based":[146],"on":[147,155],"penalty":[148],"function":[149],"approach":[150],"designed.":[152],"Some":[153],"suggestions":[154],"are":[161],"also":[162],"presented.":[163]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}