{"id":"https://openalex.org/W2098352464","doi":"https://doi.org/10.5430/air.v2n2p109","title":"Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization","display_name":"Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization","publication_year":2013,"publication_date":"2013-03-03","ids":{"openalex":"https://openalex.org/W2098352464","doi":"https://doi.org/10.5430/air.v2n2p109","mag":"2098352464"},"language":"en","primary_location":{"id":"doi:10.5430/air.v2n2p109","is_oa":true,"landing_page_url":"https://doi.org/10.5430/air.v2n2p109","pdf_url":"https://www.sciedu.ca/journal/index.php/air/article/download/1334/1404","source":{"id":"https://openalex.org/S4210167461","display_name":"Artificial Intelligence Research","issn_l":"1927-6974","issn":["1927-6974","1927-6982"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320842","host_organization_name":"Sciedu Press","host_organization_lineage":["https://openalex.org/P4310320842"],"host_organization_lineage_names":["Sciedu Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciedu.ca/journal/index.php/air/article/download/1334/1404","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112718378","display_name":"Masatoshi Sakawa","orcid":null},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masatoshi Sakawa","raw_affiliation_strings":["Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan","Hiroshima University"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan","institution_ids":["https://openalex.org/I113306721"]},{"raw_affiliation_string":"Hiroshima University","institution_ids":["https://openalex.org/I113306721"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101711254","display_name":"Takeshi Matsui","orcid":"https://orcid.org/0000-0003-4740-1824"},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takeshi Matsui","raw_affiliation_strings":["Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan","institution_ids":["https://openalex.org/I113306721"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112718378"],"corresponding_institution_ids":["https://openalex.org/I113306721"],"apc_list":null,"apc_paid":null,"fwci":3.0526,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.9181153,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2","issue":"2","first_page":null,"last_page":null},"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":0.9984999895095825,"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":0.9965000152587891,"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/linear-programming","display_name":"Linear programming","score":0.7415385842323303},{"id":"https://openalex.org/keywords/vagueness","display_name":"Vagueness","score":0.700031578540802},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6767281889915466},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.6745129227638245},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.6726933717727661},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5227753520011902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5086711049079895},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.4736151397228241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42923030257225037},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11660134792327881}],"concepts":[{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.7415385842323303},{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.700031578540802},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6767281889915466},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.6745129227638245},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.6726933717727661},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5227753520011902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5086711049079895},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.4736151397228241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42923030257225037},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11660134792327881}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5430/air.v2n2p109","is_oa":true,"landing_page_url":"https://doi.org/10.5430/air.v2n2p109","pdf_url":"https://www.sciedu.ca/journal/index.php/air/article/download/1334/1404","source":{"id":"https://openalex.org/S4210167461","display_name":"Artificial Intelligence Research","issn_l":"1927-6974","issn":["1927-6974","1927-6982"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320842","host_organization_name":"Sciedu Press","host_organization_lineage":["https://openalex.org/P4310320842"],"host_organization_lineage_names":["Sciedu Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Research","raw_type":"journal-article"},{"id":"pmh:oai:pure.iiasa.ac.at:9135","is_oa":true,"landing_page_url":null,"pdf_url":"http://pure.iiasa.ac.at/id/eprint/9135/1/IR-09-013.pdf","source":{"id":"https://openalex.org/S4306401423","display_name":"IIASA PURE (International Institute of Applied Systems Analysis)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1317774081","host_organization_name":"International Institute for Applied Systems Analysis","host_organization_lineage":["https://openalex.org/I1317774081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Monograph"}],"best_oa_location":{"id":"doi:10.5430/air.v2n2p109","is_oa":true,"landing_page_url":"https://doi.org/10.5430/air.v2n2p109","pdf_url":"https://www.sciedu.ca/journal/index.php/air/article/download/1334/1404","source":{"id":"https://openalex.org/S4210167461","display_name":"Artificial Intelligence Research","issn_l":"1927-6974","issn":["1927-6974","1927-6982"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320842","host_organization_name":"Sciedu Press","host_organization_lineage":["https://openalex.org/P4310320842"],"host_organization_lineage_names":["Sciedu Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Research","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2098352464.pdf","grobid_xml":"https://content.openalex.org/works/W2098352464.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W95563186","https://openalex.org/W1484121744","https://openalex.org/W1527514050","https://openalex.org/W1549715974","https://openalex.org/W1554018745","https://openalex.org/W1560622170","https://openalex.org/W1569990960","https://openalex.org/W1575842192","https://openalex.org/W1601972095","https://openalex.org/W1729590981","https://openalex.org/W1972038524","https://openalex.org/W1972571373","https://openalex.org/W1974379101","https://openalex.org/W1976767982","https://openalex.org/W1978718027","https://openalex.org/W1980346738","https://openalex.org/W1983688269","https://openalex.org/W1986183688","https://openalex.org/W1987420866","https://openalex.org/W1990984428","https://openalex.org/W1998763779","https://openalex.org/W1999651652","https://openalex.org/W2003285839","https://openalex.org/W2007137127","https://openalex.org/W2012724591","https://openalex.org/W2013782263","https://openalex.org/W2013841076","https://openalex.org/W2018175162","https://openalex.org/W2018528595","https://openalex.org/W2018766454","https://openalex.org/W2037065890","https://openalex.org/W2040158468","https://openalex.org/W2049433341","https://openalex.org/W2049606892","https://openalex.org/W2051594008","https://openalex.org/W2056010438","https://openalex.org/W2058265515","https://openalex.org/W2060942611","https://openalex.org/W2066194037","https://openalex.org/W2068569787","https://openalex.org/W2070491887","https://openalex.org/W2076606240","https://openalex.org/W2078552492","https://openalex.org/W2085427336","https://openalex.org/W2096126893","https://openalex.org/W2097731086","https://openalex.org/W2099867994","https://openalex.org/W2103945139","https://openalex.org/W2106467356","https://openalex.org/W2143863355","https://openalex.org/W2156577211","https://openalex.org/W2169889521","https://openalex.org/W2171715801","https://openalex.org/W2235178083","https://openalex.org/W2487138304","https://openalex.org/W2503096983","https://openalex.org/W2756405080","https://openalex.org/W3140227716","https://openalex.org/W4251495539","https://openalex.org/W4292158025","https://openalex.org/W6600680088"],"related_works":["https://openalex.org/W4205348974","https://openalex.org/W4214624958","https://openalex.org/W2337360258","https://openalex.org/W2133667137","https://openalex.org/W2784100870","https://openalex.org/W4231039027","https://openalex.org/W2007464938","https://openalex.org/W4245568382","https://openalex.org/W1838347333","https://openalex.org/W2356478177"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"two-level":[3,31],"linear":[4,32],"programming":[5,33,64],"problems":[6,34],"involving":[7],"random":[8],"variable":[9],"coefficients":[10],"both":[11,59],"in":[12,49],"objectivefunctions":[13],"and":[14,90],"constraints.":[15],"Using":[16],"the":[17,28,46,84,88,91,95,108],"concept":[18],"of":[19,43,45,87,94,107],"chance":[20],"constraints,":[21],"under":[22],"some":[23],"appropriate":[24],"assumptions":[25],"for":[26,75],"distributionfunctions,":[27],"original":[29],"stochastic":[30],"are":[35],"transformed":[36],"into":[37],"deterministic":[38],"ones.":[39],"Takinginto":[40],"account":[41],"vagueness":[42],"judgments":[44],"decision":[47],"makers,":[48],"order":[50],"to":[51,104],"derive":[52],"a":[53,76],"satisfactory":[54,77],"solution":[55,78],"consideringsatisfactory":[56],"balance":[57],"between":[58],"levels,":[60],"an":[61],"interactive":[62],"fuzzy":[63],"method":[65,70],"is":[66,102],"proposed.":[67],"The":[68],"proposed":[69,109],"hasan":[71],"advantage":[72],"that":[73],"candidates":[74],"can":[79],"be":[80],"easily":[81],"obtained":[82],"through":[83],"combined":[85],"use":[86],"bisectionmethod":[89],"phase":[92],"one":[93],"simplex":[96],"method.":[97,110],"An":[98],"illustrative":[99],"numerical":[100],"example":[101],"provided":[103],"demonstrate":[105],"thefeasibility":[106]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"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":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
