{"id":"https://openalex.org/W2039052464","doi":"https://doi.org/10.1007/s10700-012-9152-7","title":"The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers","display_name":"The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers","publication_year":2012,"publication_date":"2012-10-30","ids":{"openalex":"https://openalex.org/W2039052464","doi":"https://doi.org/10.1007/s10700-012-9152-7","mag":"2039052464"},"language":"en","primary_location":{"id":"doi:10.1007/s10700-012-9152-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-012-9152-7","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","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/A5029506482","display_name":"Behrouz Kheirfam","orcid":"https://orcid.org/0000-0001-7928-2618"},"institutions":[{"id":"https://openalex.org/I51301133","display_name":"Azarbaijan Shahid Madani University","ror":"https://ror.org/05pg2cw06","country_code":"IR","type":"education","lineage":["https://openalex.org/I51301133"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Behrouz Kheirfam","raw_affiliation_strings":["Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran","Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran","institution_ids":["https://openalex.org/I51301133"]},{"raw_affiliation_string":"Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran#TAB#","institution_ids":["https://openalex.org/I51301133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010560354","display_name":"Jos\u00e9 Lu\u00eds Verdegay","orcid":"https://orcid.org/0000-0003-2487-942X"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9-Luis Verdegay","raw_affiliation_strings":["Department of Computer Science and A.I. CITIC, Universidad de Granada, 18071, Granada, Spain","Department of Computer Science and A.I. CITIC, Universidad de Granada, Granada, Spain 18071#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and A.I. CITIC, Universidad de Granada, 18071, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Department of Computer Science and A.I. CITIC, Universidad de Granada, Granada, Spain 18071#TAB#","institution_ids":["https://openalex.org/I173304897"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2590,"currency":"EUR","value_usd":3390},"apc_paid":null,"fwci":6.253,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.96127995,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"12","issue":"2","first_page":"171","last_page":"189"},"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":0.9991999864578247,"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":0.9991999864578247,"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/linear-programming","display_name":"Linear programming","score":0.7035068869590759},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.683364987373352},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.6775913238525391},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.66938316822052},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6013485193252563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5699405670166016},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.49897265434265137},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.44961777329444885},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.41825804114341736},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.2836693823337555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2550337314605713},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09592685103416443},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.050646573305130005}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7035068869590759},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.683364987373352},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.6775913238525391},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66938316822052},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6013485193252563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5699405670166016},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.49897265434265137},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.44961777329444885},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.41825804114341736},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2836693823337555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2550337314605713},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09592685103416443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.050646573305130005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10700-012-9152-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10700-012-9152-7","pdf_url":null,"source":{"id":"https://openalex.org/S93986401","display_name":"Fuzzy Optimization and Decision Making","issn_l":"1568-4539","issn":["1568-4539","1573-2908"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fuzzy Optimization and Decision Making","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W197129600","https://openalex.org/W965656746","https://openalex.org/W1968366840","https://openalex.org/W1979718274","https://openalex.org/W1990819810","https://openalex.org/W1992980798","https://openalex.org/W2015863315","https://openalex.org/W2039796074","https://openalex.org/W2071297453","https://openalex.org/W2084300620","https://openalex.org/W2085888792","https://openalex.org/W2086393750","https://openalex.org/W2088907949","https://openalex.org/W2099867994","https://openalex.org/W2171715801","https://openalex.org/W2176210190","https://openalex.org/W2186820014","https://openalex.org/W2228932084","https://openalex.org/W2993706351","https://openalex.org/W3010279532","https://openalex.org/W4292158025"],"related_works":["https://openalex.org/W2133667137","https://openalex.org/W4385791789","https://openalex.org/W1857955804","https://openalex.org/W2022674418","https://openalex.org/W1990165789","https://openalex.org/W3187601603","https://openalex.org/W4231885858","https://openalex.org/W3108685588","https://openalex.org/W1983168083","https://openalex.org/W124472458"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}