{"id":"https://openalex.org/W1983168083","doi":"https://doi.org/10.4018/joris.2011040102","title":"Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables","display_name":"Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W1983168083","doi":"https://doi.org/10.4018/joris.2011040102","mag":"1983168083"},"language":"en","primary_location":{"id":"doi:10.4018/joris.2011040102","is_oa":false,"landing_page_url":"https://doi.org/10.4018/joris.2011040102","pdf_url":null,"source":{"id":"https://openalex.org/S176018216","display_name":"International Journal of Operations Research and Information Systems","issn_l":"1947-9328","issn":["1947-9328","1947-9336"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Operations Research and Information Systems","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/A5103925109","display_name":"Seyed Hadi Nasseri","orcid":null},"institutions":[{"id":"https://openalex.org/I4871159","display_name":"University of Mazandaran","ror":"https://ror.org/05fp9g671","country_code":"IR","type":"education","lineage":["https://openalex.org/I4871159"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Seyed Hadi Nasseri","raw_affiliation_strings":["University of Mazandaran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Mazandaran, Iran","institution_ids":["https://openalex.org/I4871159"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089713497","display_name":"Ali Ebrahimnejad","orcid":"https://orcid.org/0000-0001-6003-6601"},"institutions":[{"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":false,"raw_author_name":"Ali Ebrahimnejad","raw_affiliation_strings":["Islamic Azad University, Qaemshahr Branch, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Islamic Azad University, Qaemshahr Branch, Iran","institution_ids":["https://openalex.org/I4210138903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2068,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.95046796,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"2","first_page":"22","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994999766349792,"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":0.9972000122070312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.8026641607284546},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.7730079293251038},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.64959317445755},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6258913278579712},{"id":"https://openalex.org/keywords/revised-simplex-method","display_name":"Revised simplex method","score":0.6059750914573669},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5591793060302734},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.550559937953949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5430064797401428},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4921371340751648},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.479610800743103},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.454928994178772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3599167466163635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33720526099205017},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.2820034623146057},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1176251471042633},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06507855653762817},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.06476309895515442}],"concepts":[{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.8026641607284546},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7730079293251038},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.64959317445755},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6258913278579712},{"id":"https://openalex.org/C191157680","wikidata":"https://www.wikidata.org/wiki/Q17085895","display_name":"Revised simplex method","level":4,"score":0.6059750914573669},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5591793060302734},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.550559937953949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5430064797401428},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4921371340751648},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.479610800743103},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.454928994178772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3599167466163635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33720526099205017},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2820034623146057},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1176251471042633},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06507855653762817},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.06476309895515442},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4018/joris.2011040102","is_oa":false,"landing_page_url":"https://doi.org/10.4018/joris.2011040102","pdf_url":null,"source":{"id":"https://openalex.org/S176018216","display_name":"International Journal of Operations Research and Information Systems","issn_l":"1947-9328","issn":["1947-9328","1947-9336"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320424","host_organization_name":"IGI Global","host_organization_lineage":["https://openalex.org/P4310320424"],"host_organization_lineage_names":["IGI Global"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Operations Research and Information Systems","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:igg:joris0:v:2:y:2011:i:2:p:22-39","is_oa":false,"landing_page_url":"https://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/joris.2011040102","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1490891821","https://openalex.org/W1505076599","https://openalex.org/W1915872099","https://openalex.org/W1966884570","https://openalex.org/W1968366840","https://openalex.org/W1982109263","https://openalex.org/W1990819810","https://openalex.org/W1991841327","https://openalex.org/W1992980798","https://openalex.org/W2000327931","https://openalex.org/W2002344226","https://openalex.org/W2015863315","https://openalex.org/W2037258742","https://openalex.org/W2039796074","https://openalex.org/W2066554948","https://openalex.org/W2067833990","https://openalex.org/W2071297453","https://openalex.org/W2071782633","https://openalex.org/W2073968196","https://openalex.org/W2081677962","https://openalex.org/W2084300620","https://openalex.org/W2085888792","https://openalex.org/W2094985434","https://openalex.org/W2099867994","https://openalex.org/W2105152172","https://openalex.org/W2113532413","https://openalex.org/W2116443109","https://openalex.org/W2122895761","https://openalex.org/W2133695364","https://openalex.org/W2159480638","https://openalex.org/W2166863502","https://openalex.org/W2167988338","https://openalex.org/W2171715801","https://openalex.org/W2176210190","https://openalex.org/W2235178083","https://openalex.org/W3010279532","https://openalex.org/W3125430941","https://openalex.org/W4292158025"],"related_works":["https://openalex.org/W2477407501","https://openalex.org/W2027241495","https://openalex.org/W2385011829","https://openalex.org/W1831791463","https://openalex.org/W2082379955","https://openalex.org/W239189851","https://openalex.org/W313296872","https://openalex.org/W2117094153","https://openalex.org/W4231885858","https://openalex.org/W2480440586"],"abstract_inverted_index":{"In":[0],"the":[1,80,102,113,119],"real":[2],"word,":[3],"there":[4],"are":[5,31],"many":[6],"problems":[7,30,34,42,60,96],"which":[8],"have":[9,44],"linear":[10,32,58,94],"programming":[11,33,59,95],"models":[12,21],"and":[13,43,54,67,86],"sometimes":[14],"it":[15],"is":[16],"necessary":[17],"to":[18,73],"formulate":[19],"these":[20,29,41,50,75],"with":[22,35,61,97],"parameters":[23],"of":[24],"uncertainty.":[25],"Many":[26],"numbers":[27],"from":[28],"fuzzy":[36,63,70,84,99],"variables.":[37,100],"Some":[38],"authors":[39,103],"considered":[40,57],"developed":[45,79],"various":[46],"methods":[47],"for":[48,92,121],"solving":[49,93],"problems.":[51,76],"Recently,":[52],"Mahdavi-Amiri":[53],"Nasseri":[55],"(2007)":[56],"trapezoidal":[62,98],"data":[64],"and/or":[65],"variables":[66],"stated":[68],"a":[69,88],"simplex":[71,90,109,115,129],"algorithm":[72,91,110,117],"solve":[74],"Moreover,":[77],"they":[78],"duality":[81],"results":[82],"in":[83],"environment":[85],"presented":[87,107],"dual":[89,108],"Here,":[101],"show":[104],"that":[105],"this":[106],"directly":[111],"using":[112,127],"primal":[114,128],"tableau":[116],"tenders":[118],"capability":[120],"sensitivity":[122],"(or":[123],"post":[124],"optimality)":[125],"analysis":[126],"tableaus.":[130]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T06:19:23.411458","created_date":"2025-10-10T00:00:00"}