{"id":"https://openalex.org/W2769702904","doi":"https://doi.org/10.1007/978-0-387-74759-0_419","title":"Multi-objective Fractional Programming Problems","display_name":"Multi-objective Fractional Programming Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2769702904","doi":"https://doi.org/10.1007/978-0-387-74759-0_419","mag":"2769702904"},"language":"en","primary_location":{"id":"doi:10.1007/978-0-387-74759-0_419","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_419","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"},"type":"book-chapter","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/A5101028635","display_name":"Zhian Liang","orcid":null},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhian Liang","raw_affiliation_strings":["Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, P.R. China","institution_ids":["https://openalex.org/I181679659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101028635"],"corresponding_institution_ids":["https://openalex.org/I181679659"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36979332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2442","last_page":"2448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9976000189781189,"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":0.9833999872207642,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47091031074523926},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.4621579945087433},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.11199721693992615},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07819023728370667}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47091031074523926},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4621579945087433},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.11199721693992615},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07819023728370667},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-0-387-74759-0_419","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-0-387-74759-0_419","pdf_url":null,"source":{"id":"https://openalex.org/S4306509378","display_name":"Encyclopedia of Optimization","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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopedia of Optimization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W196661096","https://openalex.org/W1502437643","https://openalex.org/W1978649511","https://openalex.org/W1981662088","https://openalex.org/W1982328063","https://openalex.org/W2000983337","https://openalex.org/W2001156992","https://openalex.org/W2006159242","https://openalex.org/W2009446014","https://openalex.org/W2012303267","https://openalex.org/W2021157320","https://openalex.org/W2022351719","https://openalex.org/W2024600755","https://openalex.org/W2026520001","https://openalex.org/W2055394249","https://openalex.org/W2055751565","https://openalex.org/W2076214122","https://openalex.org/W2083492057","https://openalex.org/W2313488898","https://openalex.org/W2561178549","https://openalex.org/W2566900571","https://openalex.org/W4210963865","https://openalex.org/W4211114541","https://openalex.org/W4235178178","https://openalex.org/W4239992743","https://openalex.org/W4248623816","https://openalex.org/W4253679144","https://openalex.org/W4292864963"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2382290278","https://openalex.org/W2049775471","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W1596801655"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}