{"id":"https://openalex.org/W3200923033","doi":"https://doi.org/10.1007/s11590-021-01806-0","title":"A note on approximate proper efficiency in linear fractional vector optimization","display_name":"A note on approximate proper efficiency in linear fractional vector optimization","publication_year":2021,"publication_date":"2021-09-22","ids":{"openalex":"https://openalex.org/W3200923033","doi":"https://doi.org/10.1007/s11590-021-01806-0","mag":"3200923033"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-021-01806-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-021-01806-0","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","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/A5061100646","display_name":"Nguy\u1ec5n V\u0103n Tuy\u00ean","orcid":"https://orcid.org/0000-0003-1920-310X"},"institutions":[{"id":"https://openalex.org/I4210095523","display_name":"Hanoi Pedagogical University 2","ror":"https://ror.org/00st18g74","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210095523"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Nguyen Van Tuyen","raw_affiliation_strings":["Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam"],"raw_orcid":"https://orcid.org/0000-0003-1920-310X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam","institution_ids":["https://openalex.org/I4210095523"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061100646"],"corresponding_institution_ids":["https://openalex.org/I4210095523"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.1319,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.5070512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"16","issue":"6","first_page":"1835","last_page":"1845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9811000227928162,"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/computational-intelligence","display_name":"Computational intelligence","score":0.7272992134094238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6723930239677429},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6439496278762817},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.62464439868927},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5397774577140808},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5013244152069092},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47580060362815857},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4100750684738159},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.36100104451179504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27611488103866577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21033528447151184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06498092412948608},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05812704563140869}],"concepts":[{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.7272992134094238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6723930239677429},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6439496278762817},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.62464439868927},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5397774577140808},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5013244152069092},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47580060362815857},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4100750684738159},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.36100104451179504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27611488103866577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21033528447151184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06498092412948608},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05812704563140869},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-021-01806-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-021-01806-0","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5699999928474426}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W113278869","https://openalex.org/W606344609","https://openalex.org/W641923829","https://openalex.org/W828106490","https://openalex.org/W1553702074","https://openalex.org/W1977185222","https://openalex.org/W1980976739","https://openalex.org/W1986940126","https://openalex.org/W1998164448","https://openalex.org/W2015936756","https://openalex.org/W2027817473","https://openalex.org/W2036737894","https://openalex.org/W2037534711","https://openalex.org/W2047780332","https://openalex.org/W2074909374","https://openalex.org/W2083818478","https://openalex.org/W2153015072","https://openalex.org/W2163290120","https://openalex.org/W2319463865","https://openalex.org/W2517749439","https://openalex.org/W2798803384","https://openalex.org/W2802620382","https://openalex.org/W2809728774","https://openalex.org/W2982171703","https://openalex.org/W2996507251","https://openalex.org/W2999972485","https://openalex.org/W3039226795","https://openalex.org/W3044157304","https://openalex.org/W3111917985","https://openalex.org/W3159525208","https://openalex.org/W4249125060","https://openalex.org/W4249667877","https://openalex.org/W4253214256","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2766340440","https://openalex.org/W2565276936","https://openalex.org/W4385713703","https://openalex.org/W109016340","https://openalex.org/W179906810","https://openalex.org/W188711498","https://openalex.org/W2390455111","https://openalex.org/W1992155926","https://openalex.org/W3199277564","https://openalex.org/W2013374813"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}