{"id":"https://openalex.org/W2094779154","doi":"https://doi.org/10.1007/s10700-009-9049-2","title":"The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions","display_name":"The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions","publication_year":2009,"publication_date":"2009-02-07","ids":{"openalex":"https://openalex.org/W2094779154","doi":"https://doi.org/10.1007/s10700-009-9049-2","mag":"2094779154"},"language":"en","primary_location":{"id":"doi:10.1007/s10700-009-9049-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-009-9049-2","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","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/A5061684739","display_name":"Hsien-Chung Wu","orcid":"https://orcid.org/0000-0003-0284-3303"},"institutions":[{"id":"https://openalex.org/I135551196","display_name":"National Kaohsiung Normal University","ror":"https://ror.org/04tsc8g87","country_code":"TW","type":"education","lineage":["https://openalex.org/I135551196"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Hsien-Chung Wu","raw_affiliation_strings":["Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan 802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan 802","institution_ids":["https://openalex.org/I135551196"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061684739"],"corresponding_institution_ids":["https://openalex.org/I135551196"],"apc_list":{"value":2590,"currency":"EUR","value_usd":3390},"apc_paid":null,"fwci":0.2831,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.63078119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":"1","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9987999796867371,"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":0.9640496969223022},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.786860466003418},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6494783163070679},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5882600545883179},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5160410404205322},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4726760983467102},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.276139497756958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16859105229377747},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07967719435691833}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9640496969223022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.786860466003418},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6494783163070679},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5882600545883179},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5160410404205322},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4726760983467102},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.276139497756958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16859105229377747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07967719435691833}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10700-009-9049-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-009-9049-2","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W202383464","https://openalex.org/W580032574","https://openalex.org/W1484121744","https://openalex.org/W1505076599","https://openalex.org/W1549715974","https://openalex.org/W1557098843","https://openalex.org/W1569990960","https://openalex.org/W1575842192","https://openalex.org/W1738394416","https://openalex.org/W1983688269","https://openalex.org/W1986060983","https://openalex.org/W2041614165","https://openalex.org/W2078839838","https://openalex.org/W2113688222","https://openalex.org/W2157041604","https://openalex.org/W2235178083","https://openalex.org/W2293574808","https://openalex.org/W2301746362","https://openalex.org/W2798344481","https://openalex.org/W2912565176","https://openalex.org/W3000651840","https://openalex.org/W4211007335","https://openalex.org/W4229703161","https://openalex.org/W4235178178","https://openalex.org/W4298380944","https://openalex.org/W4379373144"],"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/W4210398350","https://openalex.org/W2593574046","https://openalex.org/W2797479470","https://openalex.org/W2120257557"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2025-10-10T00:00:00"}