{"id":"https://openalex.org/W2097236828","doi":"https://doi.org/10.1109/icsmc.2009.5346825","title":"On positioned solution of linear programming with grey parameters","display_name":"On positioned solution of linear programming with grey parameters","publication_year":2009,"publication_date":"2009-10-01","ids":{"openalex":"https://openalex.org/W2097236828","doi":"https://doi.org/10.1109/icsmc.2009.5346825","mag":"2097236828"},"language":"en","primary_location":{"id":"doi:10.1109/icsmc.2009.5346825","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icsmc.2009.5346825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Systems, Man and Cybernetics","raw_type":"proceedings-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/A5070239285","display_name":"Sifeng Liu","orcid":"https://orcid.org/0000-0002-5872-9457"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sifeng Liu Yaoguo Dang","raw_affiliation_strings":["Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China","Institute for Grey Systems Studies,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)"],"affiliations":[{"raw_affiliation_string":"Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"Institute for Grey Systems Studies,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040263855","display_name":"Jeffrey Yi\u2010Lin Forrest","orcid":"https://orcid.org/0000-0002-5124-9012"},"institutions":[{"id":"https://openalex.org/I169494899","display_name":"Slippery Rock University","ror":"https://ror.org/0369st156","country_code":"US","type":"education","lineage":["https://openalex.org/I169494899"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey Forrest","raw_affiliation_strings":["Int. Institute for General Systems Studies, Slippery Rock University, Slippery Rock, PA, USA","Int. Institute for General Systems Studies, Slippery Rock University, Slippery Rock, PA 16057, USA"],"affiliations":[{"raw_affiliation_string":"Int. Institute for General Systems Studies, Slippery Rock University, Slippery Rock, PA, USA","institution_ids":["https://openalex.org/I169494899"]},{"raw_affiliation_string":"Int. Institute for General Systems Studies, Slippery Rock University, Slippery Rock, PA 16057, USA","institution_ids":["https://openalex.org/I169494899"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070239285"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":0.8334,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.78072299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"751","last_page":"756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12368","display_name":"Grey System Theory Applications","score":0.9911999702453613,"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"}},"topics":[{"id":"https://openalex.org/T12368","display_name":"Grey System Theory Applications","score":0.9911999702453613,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.953499972820282,"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":0.9354000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.8291968107223511},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.625957190990448},{"id":"https://openalex.org/keywords/basic-solution","display_name":"Basic solution","score":0.5879724025726318},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.542945384979248},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5168050527572632},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.49436020851135254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48594415187835693},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4715326428413391},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4413684904575348},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.44073253870010376},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42240458726882935},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08008873462677002}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.8291968107223511},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.625957190990448},{"id":"https://openalex.org/C126706214","wikidata":"https://www.wikidata.org/wiki/Q4867053","display_name":"Basic solution","level":4,"score":0.5879724025726318},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.542945384979248},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5168050527572632},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.49436020851135254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48594415187835693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4715326428413391},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4413684904575348},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.44073253870010376},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42240458726882935},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08008873462677002},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C52859227","wikidata":"https://www.wikidata.org/wiki/Q7877","display_name":"Electrochemistry","level":3,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icsmc.2009.5346825","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icsmc.2009.5346825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Systems, Man and Cybernetics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W114122946","https://openalex.org/W182476373","https://openalex.org/W1984349093","https://openalex.org/W2396705308"],"related_works":["https://openalex.org/W2126096360","https://openalex.org/W4386394964","https://openalex.org/W2379720599","https://openalex.org/W3092736858","https://openalex.org/W2368660077","https://openalex.org/W4245568382","https://openalex.org/W90125000","https://openalex.org/W4205332774","https://openalex.org/W2389404837","https://openalex.org/W2394376027"],"abstract_inverted_index":{"To":[0],"surmount":[1],"the":[2,6,22,26,29,44,50,56,59,62,72,76,80,85,102,109],"difficulty":[3,99],"in":[4,100],"solving":[5,101],"problem":[7,41,87,104],"of":[8,17,42,52,58,61,79,94],"linear":[9,24,96],"programming":[10,74],"with":[11],"grey":[12],"parameters":[13],"(LPGP),":[14],"a":[15,115],"series":[16],"new":[18,35],"conceptions":[19],"such":[20],"as":[21],"positioned":[23,53,64,73],"programming,":[25],"ideal":[27],"model,":[28,31],"critical":[30],"and":[32,55,75,105],"some":[33],"other":[34],"ideas":[36],"are":[37,66],"put":[38],"forward.":[39],"The":[40,68,98],"how":[43,106],"optimum":[45,63],"solution":[46,70,81,110],"is":[47],"affected":[48],"by":[49],"variation":[51,60],"coefficients":[54],"range":[57],"values":[65],"studied.":[67],"satisfying":[69,77],"for":[71],"degree":[78],"were":[82],"defined.":[83],"Thus,":[84],"LPGP":[86,103],"will":[88],"be":[89],"converted":[90],"into":[91],"several":[92],"problems":[93],"ordinary":[95],"programming.":[97],"to":[107,114],"appraise":[108],"have":[111],"been":[112],"surmounted":[113],"certain":[116],"degree.":[117]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}
