{"id":"https://openalex.org/W3194545263","doi":"https://doi.org/10.3390/sym13091572","title":"Bifuzzy-Bilevel Programming Model: Solution and Application","display_name":"Bifuzzy-Bilevel Programming Model: Solution and Application","publication_year":2021,"publication_date":"2021-08-26","ids":{"openalex":"https://openalex.org/W3194545263","doi":"https://doi.org/10.3390/sym13091572","mag":"3194545263"},"language":"en","primary_location":{"id":"doi:10.3390/sym13091572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091572","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1572/pdf?version=1629977195","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/9/1572/pdf?version=1629977195","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100434474","display_name":"Jiahao Chen","orcid":"https://orcid.org/0000-0002-5449-155X"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahao Chen","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084715077","display_name":"Yujiao Jiang","orcid":"https://orcid.org/0000-0003-4599-024X"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yujiao Jiang","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067037706","display_name":"Wang Guang","orcid":"https://orcid.org/0000-0002-4515-8536"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guang Wang","raw_affiliation_strings":["School of Management, Shanghai University, Shanghai 200444, China"],"affiliations":[{"raw_affiliation_string":"School of Management, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084715077"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1383,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44682257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"9","first_page":"1572","last_page":"1572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9987999796867371,"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":0.9987999796867371,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.994700014591217,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8791358470916748},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7226160764694214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6629117727279663},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5606921911239624},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.491458535194397},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.4764407277107239},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.470051646232605},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4541546404361725},{"id":"https://openalex.org/keywords/programming-paradigm","display_name":"Programming paradigm","score":0.4364071786403656},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.4215197265148163},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.26878622174263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24630647897720337},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24580031633377075},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1653885841369629}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8791358470916748},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7226160764694214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6629117727279663},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5606921911239624},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.491458535194397},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.4764407277107239},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.470051646232605},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4541546404361725},{"id":"https://openalex.org/C34165917","wikidata":"https://www.wikidata.org/wiki/Q188267","display_name":"Programming paradigm","level":2,"score":0.4364071786403656},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4215197265148163},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.26878622174263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24630647897720337},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24580031633377075},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1653885841369629},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"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},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13091572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091572","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1572/pdf?version=1629977195","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:024afb6ee1634f58b2c1382e51938d5e","is_oa":true,"landing_page_url":"https://doaj.org/article/024afb6ee1634f58b2c1382e51938d5e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 9, p 1572 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/9/1572/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13091572","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 9; Pages: 1572","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13091572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091572","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1572/pdf?version=1629977195","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6401056344","display_name":null,"funder_award_id":"71872110","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3194545263.pdf","grobid_xml":"https://content.openalex.org/works/W3194545263.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W198381359","https://openalex.org/W1676470423","https://openalex.org/W1979464927","https://openalex.org/W2009649383","https://openalex.org/W2031264011","https://openalex.org/W2061233843","https://openalex.org/W2075212150","https://openalex.org/W2082350576","https://openalex.org/W2082793626","https://openalex.org/W2089135228","https://openalex.org/W2097635199","https://openalex.org/W2113276388","https://openalex.org/W2128530362","https://openalex.org/W2146576699","https://openalex.org/W2160476305","https://openalex.org/W2274279545","https://openalex.org/W2293172648","https://openalex.org/W2325107122","https://openalex.org/W2477392334","https://openalex.org/W2481910659","https://openalex.org/W2618162153","https://openalex.org/W2716585405","https://openalex.org/W3025803191","https://openalex.org/W3143971390","https://openalex.org/W3192182267","https://openalex.org/W6669515618","https://openalex.org/W6671246963","https://openalex.org/W6676848793","https://openalex.org/W6701307947"],"related_works":["https://openalex.org/W2354737650","https://openalex.org/W2392236356","https://openalex.org/W2015124671","https://openalex.org/W2136118765","https://openalex.org/W2061228544","https://openalex.org/W2374070196","https://openalex.org/W2182614003","https://openalex.org/W2371017651","https://openalex.org/W2360642173","https://openalex.org/W2131023196"],"abstract_inverted_index":{"Bi-level":[0],"programming":[1,44,74,89,140],"is":[2,53,91,142],"widely":[3],"used":[4],"in":[5,20,55,144,172],"processing":[6],"various":[7],"questions,":[8],"but":[9],"it":[10],"cannot":[11],"deal":[12],"with":[13,29],"the":[14,48,68,78,81,83,87,95,101,107,109,121,127,133,138,157,163,169,173,182,185],"complex":[15,61],"and":[16,31,66,70,103,112,152,165,168],"fuzzy":[17],"information":[18,33,171],"contained":[19],"problems.":[21],"In":[22],"order":[23],"to":[24,50,100,119,146],"solve":[25],"such":[26],"problems":[27],"better":[28],"intricate":[30,149],"vague":[32],"that":[34,46],"can":[35,59,175],"be":[36,177],"efficiently":[37],"handled":[38],"by":[39,93,125],"bifuzzy":[40,51,170],"theory,":[41],"a":[42],"bifuzzy\u2013bilevel":[43,88,139],"model":[45,90,141],"sets":[47],"parameters":[49],"variables":[52],"proposed":[54,186],"this":[56],"paper,":[57],"which":[58,180],"process":[60],"realistic":[62],"data":[63],"more":[64],"accurately":[65],"improve":[67],"feasibility":[69],"validity":[71],"of":[72,80,86,106,132,160,184],"bi-level":[73],"models.":[75],"To":[76],"ensure":[77],"solvability":[79],"model,":[82,108],"equivalent":[84],"form":[85],"obtained":[92],"utilizing":[94],"expected":[96],"value":[97],"operator.":[98],"According":[99],"linear":[102],"nonlinear":[104],"characteristics":[105],"Karush\u2013Kuhn\u2013Tucker":[110],"condition":[111],"particle":[113],"swarm":[114],"optimization":[115],"algorithm":[116],"are":[117],"employed":[118],"handle":[120],"problem,":[122],"respectively.":[123],"Finally,":[124],"taking":[126],"distribution":[128],"center":[129],"location":[130],"problem":[131,174],"supplier":[134],"as":[135],"an":[136],"example,":[137],"applied":[143],"practice":[145],"balance":[147],"highly":[148],"customer":[150],"demands":[151],"corporate":[153],"cost":[154],"minimization,":[155],"obtaining":[156],"feasible":[158],"solution":[159],"functions":[161],"at":[162],"upper":[164],"lower":[166],"levels,":[167],"also":[176],"processed":[178],"well,":[179],"proves":[181],"effectiveness":[183],"methodology.":[187]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}