{"id":"https://openalex.org/W2092464556","doi":"https://doi.org/10.4236/am.2011.26089","title":"A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers","display_name":"A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2092464556","doi":"https://doi.org/10.4236/am.2011.26089","mag":"2092464556"},"language":"en","primary_location":{"id":"doi:10.4236/am.2011.26089","doi":"https://doi.org/10.4236/am.2011.26089","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2011.26089","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=5282","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=5282","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089713497","display_name":"Ali Ebrahimnejad","orcid":"https://orcid.org/0000-0001-6003-6601","observed_orcids":["https://orcid.org/0000-0001-6003-6601"]},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]},{"id":"https://openalex.org/I4210138903","display_name":"Qaemshahr Islamic Azad University","ror":"https://ror.org/03y0dv989","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210138903"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ali Ebrahimnejad","raw_affiliation_strings":["Department of Mathematics , Qaemshahr Branch , Islamic Azad University , Qaemshar , Iran","Islamic Azad University, Science and Research Branch, Tehran,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Qaemshahr Branch , Islamic Azad University , Qaemshar , Iran","institution_ids":["https://openalex.org/I4210138903"]},{"raw_affiliation_string":"Islamic Azad University, Science and Research Branch, Tehran,","institution_ids":["https://openalex.org/I155419210"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089713497"],"corresponding_institution_ids":["https://openalex.org/I155419210","https://openalex.org/I4210138903"],"apc_list":null,"apc_paid":null,"fwci":1.6082,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83226447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"02","issue":"06","first_page":"676","last_page":"684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9916999936103821,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9916999936103821,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.007499999832361937,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.00039999998989515007,"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/fuzzy-linear-programming","display_name":"fuzzy linear programming","score":0.9649999737739563},{"id":"https://openalex.org/keywords/initial-basic-feasible-solution","display_name":"initial basic feasible solution","score":0.7450000047683716},{"id":"https://openalex.org/keywords/fuzzy-numbers","display_name":"fuzzy numbers","score":0.3199999928474426}],"concepts":[{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.8128221035003662},{"id":"https://openalex.org/C191157680","wikidata":"https://www.wikidata.org/wiki/Q17085895","display_name":"Revised simplex method","level":4,"score":0.7715011835098267},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7317106127738953},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6293829679489136},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6287943124771118},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6095341444015503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5662209391593933},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5491424798965454},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5254917740821838},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.4643882215023041},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42420464754104614},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38796859979629517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36540672183036804},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.3526642918586731},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.25241950154304504},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09553435444831848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05360668897628784},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4236/am.2011.26089","doi":"https://doi.org/10.4236/am.2011.26089","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2011.26089","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=5282","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4236/am.2011.26089","doi":"https://doi.org/10.4236/am.2011.26089","is_oa":true,"landing_page_url":"https://doi.org/10.4236/am.2011.26089","pdf_url":"http://www.scirp.org/journal/PaperDownload.aspx?paperID=5282","source":{"id":"https://openalex.org/S4210211746","display_name":"Applied Mathematics","issn_l":"2152-7385","issn":["2152-7385","2152-7393"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/P4310320480","host_organization_name":"Scientific Research Publishing","host_organization_lineage":["https://openalex.org/P4310320480"],"host_organization_lineage_names":["Scientific Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335092","display_name":"Islamic Azad University, Qaemshahr Branch","ror":"https://ror.org/03y0dv989"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2092464556.pdf","grobid_xml":"https://content.openalex.org/works/W2092464556.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1966884570","https://openalex.org/W1982109263","https://openalex.org/W1990819810","https://openalex.org/W1991841327","https://openalex.org/W1992980798","https://openalex.org/W2000171585","https://openalex.org/W2002344226","https://openalex.org/W2027029401","https://openalex.org/W2037258742","https://openalex.org/W2041891087","https://openalex.org/W2073968196","https://openalex.org/W2079501445","https://openalex.org/W2084300620","https://openalex.org/W2086393750","https://openalex.org/W2122895761","https://openalex.org/W2133695364","https://openalex.org/W2166863502","https://openalex.org/W2167988338","https://openalex.org/W2169271751","https://openalex.org/W2186820014","https://openalex.org/W2641167983","https://openalex.org/W2912565176","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2047009844","https://openalex.org/W2079501445","https://openalex.org/W2166863502","https://openalex.org/W2746997527","https://openalex.org/W1516528532","https://openalex.org/W1969104333","https://openalex.org/W1932993054","https://openalex.org/W2591569330","https://openalex.org/W2760103447","https://openalex.org/W2039052464"],"abstract_inverted_index":{"Two":[0],"existing":[1],"methods":[2],"for":[3],"solving":[4],"a":[5,57,84],"class":[6],"of":[7],"fuzzy":[8,16,28,40],"linear":[9,23],"programming":[10,24],"(FLP)":[11],"problems":[12,25],"involving":[13],"symmetric":[14],"trapezoidal":[15],"numbers":[17],"without":[18],"converting":[19],"them":[20],"to":[21,72,92,101],"crisp":[22],"are":[26],"the":[27,39,68,88,103],"primal":[29,58],"simplex":[30,42,90],"method":[31,43,52,70],"proposed":[32,44,104],"by":[33,45],"Ganesan":[34],"and":[35,38,47,67],"Veeramani":[36],"[1]":[37],"dual":[41,75],"Ebrahimnejad":[46],"Nasseri":[48],"[2].":[49],"The":[50],"former":[51],"is":[53,62,99],"not":[54,63],"applicable":[55],"when":[56],"basic":[59,76],"feasible":[60,77],"solution":[61],"easily":[64],"at":[65],"hand":[66],"later":[69],"needs":[71],"an":[73],"initial":[74],"solution.":[78],"In":[79],"this":[80],"paper,":[81],"we":[82],"develop":[83],"novel":[85],"approach":[86],"namely":[87],"primal-dual":[89],"algorithm":[91],"overcome":[93],"mentioned":[94],"shortcomings.":[95],"A":[96],"numerical":[97],"example":[98],"given":[100],"illustrate":[102],"approach.":[105]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
