{"id":"https://openalex.org/W2742734058","doi":"https://doi.org/10.1155/2017/1242841","title":"The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers","display_name":"The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2742734058","doi":"https://doi.org/10.1155/2017/1242841","mag":"2742734058"},"language":"en","primary_location":{"id":"doi:10.1155/2017/1242841","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/1242841","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/1242841.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2017/1242841.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069006681","display_name":"Nanxiang Yu","orcid":"https://orcid.org/0000-0002-4812-9693"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nanxiang Yu","raw_affiliation_strings":["College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023158018","display_name":"Dong Qiu","orcid":"https://orcid.org/0000-0002-4088-5371"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dong Qiu","raw_affiliation_strings":["College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China"],"raw_orcid":"https://orcid.org/0000-0002-4088-5371","affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023158018"],"corresponding_institution_ids":["https://openalex.org/I10535382"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.2394,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60104161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2017","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.996999979019165,"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.9820268154144287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6844078302383423},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6727863550186157},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6236658692359924},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5799975395202637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5044525861740112},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46942025423049927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2340848445892334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16619542241096497},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11098727583885193}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9820268154144287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6844078302383423},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6727863550186157},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6236658692359924},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5799975395202637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5044525861740112},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46942025423049927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2340848445892334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16619542241096497},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11098727583885193},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2017/1242841","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/1242841","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/1242841.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:1242841","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2017/1242841.xml","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"},{"id":"pmh:oai:doaj.org/article:252c5c0dff514741bb95c6860426ba1a","is_oa":false,"landing_page_url":"https://doaj.org/article/252c5c0dff514741bb95c6860426ba1a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2017 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2017/1242841","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2017/1242841","pdf_url":"http://downloads.hindawi.com/journals/complexity/2017/1242841.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1322390581","display_name":null,"funder_award_id":"11671001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1596796317","display_name":null,"funder_award_id":"cstc2015jcyjA00034","funder_id":"https://openalex.org/F4320327726","funder_display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G1668158002","display_name":null,"funder_award_id":"cstc2015jcyjA00034","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G17598817","display_name":null,"funder_award_id":"cstc2014jcyjA00054","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G1984895750","display_name":null,"funder_award_id":"11671001","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G365902072","display_name":null,"funder_award_id":"YJG143010","funder_id":"https://openalex.org/F4320327726","funder_display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G3980166096","display_name":null,"funder_award_id":"cstc2015jcyjA00034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G508836029","display_name":null,"funder_award_id":"YJG143010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5824896643","display_name":null,"funder_award_id":"cstc2014jcyjA00054","funder_id":"https://openalex.org/F4320327726","funder_display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G6314486612","display_name":null,"funder_award_id":"61472056","funder_id":"https://openalex.org/F4320327726","funder_display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G6778797647","display_name":null,"funder_award_id":"cstc2014jcyjA00054","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6924506399","display_name":null,"funder_award_id":"61472056","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"},{"id":"https://openalex.org/G7837637203","display_name":null,"funder_award_id":"11671001","funder_id":"https://openalex.org/F4320327726","funder_display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G8510573283","display_name":null,"funder_award_id":"cstc2015jcyjA00034","funder_id":"https://openalex.org/F4320321550","funder_display_name":"Chongqing Science and Technology Commission"},{"id":"https://openalex.org/G8862505326","display_name":null,"funder_award_id":"61472056","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G915750901","display_name":null,"funder_award_id":"YJG143010","funder_id":"https://openalex.org/F4320324805","funder_display_name":"Chongqing Municipal Education Commission"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321550","display_name":"Chongqing Science and Technology Commission","ror":"https://ror.org/05w9erc61"},{"id":"https://openalex.org/F4320324805","display_name":"Chongqing Municipal Education Commission","ror":"https://ror.org/031nm5713"},{"id":"https://openalex.org/F4320327726","display_name":"Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2742734058.pdf","grobid_xml":"https://content.openalex.org/works/W2742734058.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1968826977","https://openalex.org/W1995580872","https://openalex.org/W1996452001","https://openalex.org/W1997903931","https://openalex.org/W2013187986","https://openalex.org/W2013646003","https://openalex.org/W2015231239","https://openalex.org/W2027887682","https://openalex.org/W2037925185","https://openalex.org/W2038063781","https://openalex.org/W2039064061","https://openalex.org/W2056023144","https://openalex.org/W2068538505","https://openalex.org/W2074656786","https://openalex.org/W2078839838","https://openalex.org/W2079466078","https://openalex.org/W2080974154","https://openalex.org/W2099867994","https://openalex.org/W2112133207","https://openalex.org/W2168702340","https://openalex.org/W4211007335","https://openalex.org/W4239496270","https://openalex.org/W4239991171","https://openalex.org/W4245152641","https://openalex.org/W4292158025","https://openalex.org/W4361744895","https://openalex.org/W4376453274"],"related_works":["https://openalex.org/W4313491493","https://openalex.org/W2806604749","https://openalex.org/W4381489587","https://openalex.org/W4379919368","https://openalex.org/W3173427300","https://openalex.org/W3029600049","https://openalex.org/W2593574046","https://openalex.org/W4210398350","https://openalex.org/W2951068194","https://openalex.org/W4299317744"],"abstract_inverted_index":{"We":[0],"propose":[1],"the":[2,6,11,27],"solution":[3],"concepts":[4],"for":[5],"fuzzy":[7,15],"optimization":[8],"problems":[9],"in":[10],"quotient":[12],"space":[13],"of":[14],"numbers.":[16],"The":[17,31],"Karush-Kuhn-Tucker":[18],"(KKT)":[19],"optimality":[20],"conditions":[21],"are":[22],"elicited":[23],"naturally":[24],"by":[25,35],"introducing":[26],"Lagrange":[28],"function":[29],"multipliers.":[30],"effectiveness":[32],"is":[33],"illustrated":[34],"examples.":[36]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
