{"id":"https://openalex.org/W2169305915","doi":"https://doi.org/10.1080/00207720902974538","title":"A goal programming approach for fuzzy multiobjective fractional programming problems","display_name":"A goal programming approach for fuzzy multiobjective fractional programming problems","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2169305915","doi":"https://doi.org/10.1080/00207720902974538","mag":"2169305915"},"language":"en","primary_location":{"id":"doi:10.1080/00207720902974538","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720902974538","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5044235417","display_name":"Ching\u2010Ter Chang","orcid":"https://orcid.org/0000-0001-8137-8838"},"institutions":[{"id":"https://openalex.org/I173093425","display_name":"Chang Gung University","ror":"https://ror.org/00d80zx46","country_code":"TW","type":"education","lineage":["https://openalex.org/I173093425"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Ching-Ter Chang","raw_affiliation_strings":["Department of Information Management, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan, 333, Taiwan, R.O.C","Department of Information Management , Chang Gung University , 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan, 333, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Management, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan, 333, Taiwan, R.O.C","institution_ids":["https://openalex.org/I173093425"]},{"raw_affiliation_string":"Department of Information Management , Chang Gung University , 259 Wen-Hwa 1st Road, Kwei-Shan, Tao-Yuan, 333, Taiwan, R.O.C","institution_ids":["https://openalex.org/I173093425"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044235417"],"corresponding_institution_ids":["https://openalex.org/I173093425"],"apc_list":null,"apc_paid":null,"fwci":3.2639,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93047066,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"8","first_page":"867","last_page":"874"},"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9713000059127808,"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":0.932200014591217,"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/vagueness","display_name":"Vagueness","score":0.6085806488990784},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5991251468658447},{"id":"https://openalex.org/keywords/goal-programming","display_name":"Goal programming","score":0.5615437626838684},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5489611029624939},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5295326113700867},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5025560855865479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4866081476211548},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4834171533584595},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.46873030066490173},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.4509822130203247},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.44809040427207947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41688892245292664},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.4121139645576477},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3505926728248596},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.2945995330810547},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2799069285392761},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09337833523750305},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.05534985661506653}],"concepts":[{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.6085806488990784},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5991251468658447},{"id":"https://openalex.org/C61157135","wikidata":"https://www.wikidata.org/wiki/Q1345279","display_name":"Goal programming","level":2,"score":0.5615437626838684},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5489611029624939},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5295326113700867},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5025560855865479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4866081476211548},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4834171533584595},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.46873030066490173},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4509822130203247},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.44809040427207947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41688892245292664},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.4121139645576477},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3505926728248596},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2945995330810547},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2799069285392761},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09337833523750305},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.05534985661506653},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207720902974538","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720902974538","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W580032574","https://openalex.org/W1978163112","https://openalex.org/W1981915376","https://openalex.org/W1983421222","https://openalex.org/W1995681262","https://openalex.org/W1999571264","https://openalex.org/W2000348837","https://openalex.org/W2001761698","https://openalex.org/W2014571690","https://openalex.org/W2019633452","https://openalex.org/W2023023598","https://openalex.org/W2028356014","https://openalex.org/W2032845585","https://openalex.org/W2037065890","https://openalex.org/W2042229011","https://openalex.org/W2050130693","https://openalex.org/W2059740345","https://openalex.org/W2063543218","https://openalex.org/W2064817890","https://openalex.org/W2067171884","https://openalex.org/W2067954977","https://openalex.org/W2078320524","https://openalex.org/W2089624359","https://openalex.org/W2099867994","https://openalex.org/W2156577211","https://openalex.org/W2197396894","https://openalex.org/W4206663876","https://openalex.org/W4211114541","https://openalex.org/W4229703161","https://openalex.org/W4236702176","https://openalex.org/W4253679144","https://openalex.org/W4379373144"],"related_works":["https://openalex.org/W2026862346","https://openalex.org/W1557588340","https://openalex.org/W2674573885","https://openalex.org/W2167016330","https://openalex.org/W2514406964","https://openalex.org/W2953498143","https://openalex.org/W3087238649","https://openalex.org/W2613791316","https://openalex.org/W2553670024","https://openalex.org/W2517267677"],"abstract_inverted_index":{"Fuzzy":[0,40,49],"multiple":[1,110],"objective":[2,111,169],"fractional":[3,114,168],"programming":[4,31,90,99,115],"(FMOFP)":[5],"is":[6,105,127,151,195],"an":[7],"important":[8],"technique":[9],"for":[10,166],"solving":[11,180],"many":[12],"real-world":[13,193],"problems":[14],"involving":[15,73],"the":[16,24,74,86,95,120,143,157,167,171,176,181,186,189],"nature":[17],"of":[18,26,29,39,76,82,88,97,122,161,188],"vagueness,":[19],"imprecision":[20],"and/or":[21],"random.":[22],"Following":[23],"idea":[25],"binary":[27,98,113,149],"behaviour":[28,87,96],"fuzzy":[30,77,89,109,163],"(Chang":[32],"2007":[33],"Chang,":[34],"C-T.":[35],"2007.":[36],"Binary":[37],"Behavior":[38],"Programming":[41],"with":[42],"Piecewise":[43],"Membership":[44],"Functions.":[45],"IEEE":[46],"Transactions":[47],"on":[48,71],"Systems,":[50],"15:":[51],"342\u2013349.":[52],"[Crossref]":[53],",":[54],"[Google":[55],"Scholar]),":[56],"there":[57],"may":[58,84],"exist":[59],"a":[60,63,69,108,138,192],"situation":[61],"where":[62],"decision-maker":[64],"would":[65],"like":[66],"to":[67,119,141],"make":[68],"decision":[70],"FMOFP":[72],"achievement":[75],"goals,":[78],"in":[79,146],"which":[80,147],"some":[81],"them":[83],"meet":[85],"(i.e.":[91,100],"level":[92],"achieved)":[93],"or":[94],"completely":[101],"not":[102,128,152],"achieved).":[103],"This":[104],"turned":[106],"into":[107],"mixed":[112],"(FMOMBFP)":[116],"problem.":[117,183],"However,":[118],"best":[121],"our":[123],"knowledge,":[124],"this":[125,135],"problem":[126,145],"well":[129],"formulated":[130],"by":[131],"mathematical":[132],"programming.":[133],"Therefore,":[134],"article":[136],"proposes":[137],"linearisation":[139],"strategy":[140],"formulate":[142],"FMOMBFP":[144,182],"extra":[148],"variable":[150],"required.":[153],"In":[154],"addition,":[155],"achieving":[156],"highest":[158],"membership":[159],"value":[160],"each":[162],"goal":[164],"defined":[165],"function,":[170],"proposed":[172,190],"method":[173],"can":[174],"alleviate":[175],"computational":[177],"difficulties":[178],"when":[179],"To":[184],"demonstrate":[185],"usefulness":[187],"method,":[191],"case":[194],"also":[196],"included.":[197]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
