{"id":"https://openalex.org/W2791171332","doi":"https://doi.org/10.1051/ro/2018018","title":"Bi-objective mean\u2013variance method based on Chebyshev inequality bounds for multi-objective stochastic problems","display_name":"Bi-objective mean\u2013variance method based on Chebyshev inequality bounds for multi-objective stochastic problems","publication_year":2018,"publication_date":"2018-03-02","ids":{"openalex":"https://openalex.org/W2791171332","doi":"https://doi.org/10.1051/ro/2018018","mag":"2791171332"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2018018","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2018018","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2018/04/ro160288.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2018/04/ro160288.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011773855","display_name":"Hannan Amoozad Mahdiraji","orcid":"https://orcid.org/0000-0002-8382-6603"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hannan Amoozad Mahdiraji","raw_affiliation_strings":["University of Tehran, Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0002-8382-6603","affiliations":[{"raw_affiliation_string":"University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077713532","display_name":"Seyed Hossein Razavi Hajiagha","orcid":"https://orcid.org/0000-0003-2084-7244"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Seyed Hossein Razavi Hajiagha","raw_affiliation_strings":["University of Tehran, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101451847","display_name":"Shide Sadat Hashemi","orcid":"https://orcid.org/0000-0002-1907-1541"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Shide Sadat Hashemi","raw_affiliation_strings":["University of Tehran, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051206308","display_name":"Edmundas Kazimieras Zavadskas","orcid":"https://orcid.org/0000-0002-3201-949X"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Edmundas Kazimieras Zavadskas","raw_affiliation_strings":["University of Tehran, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tehran, Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011773855"],"corresponding_institution_ids":["https://openalex.org/I23946033"],"apc_list":null,"apc_paid":null,"fwci":0.7491,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71267756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"4-5","first_page":"1201","last_page":"1217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9972000122070312,"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":0.9972000122070312,"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/T10969","display_name":"Water resources management and optimization","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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":0.9890000224113464,"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.6848303079605103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.678641676902771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6471068263053894},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.6136361360549927},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.5743012428283691},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5441400408744812},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5214459300041199},{"id":"https://openalex.org/keywords/chebyshevs-inequality","display_name":"Chebyshev's inequality","score":0.4846075475215912},{"id":"https://openalex.org/keywords/multidimensional-chebyshevs-inequality","display_name":"Multidimensional Chebyshev's inequality","score":0.4806765019893646},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.47320741415023804},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4214164912700653},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.41129976511001587},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.3820027709007263},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3517330288887024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30056270956993103},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.15127089619636536},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11407974362373352}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.6848303079605103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.678641676902771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6471068263053894},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.6136361360549927},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.5743012428283691},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5441400408744812},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5214459300041199},{"id":"https://openalex.org/C71564387","wikidata":"https://www.wikidata.org/wiki/Q249514","display_name":"Chebyshev's inequality","level":5,"score":0.4846075475215912},{"id":"https://openalex.org/C201421709","wikidata":"https://www.wikidata.org/wiki/Q6934653","display_name":"Multidimensional Chebyshev's inequality","level":5,"score":0.4806765019893646},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.47320741415023804},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4214164912700653},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.41129976511001587},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3820027709007263},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3517330288887024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30056270956993103},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.15127089619636536},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11407974362373352},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1051/ro/2018018","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2018018","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2018/04/ro160288.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:dora.dmu.ac.uk:2086/20420","is_oa":false,"landing_page_url":"https://dora.dmu.ac.uk/handle/2086/20420","pdf_url":null,"source":{"id":"https://openalex.org/S4306400394","display_name":"DMU Open Research Archive (De Montfort University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66943878","host_organization_name":"De Montfort University","host_organization_lineage":["https://openalex.org/I66943878"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:numdam.org:RO_2018__52_4-5_1201_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2018018/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/dc364911-7588-485b-a508-c129fd4294f9","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/dc364911-7588-485b-a508-c129fd4294f9","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mahdiraji , H A , Hajiagha , S H R , Hashemi , S S & Zavadskas , E K 2018 , ' Bi-objective mean\u2013variance method based on Chebyshev inequality bounds for multi-objective stochastic problems ' , RAIRO - Operations Research , vol. 52 , no. 4 , pp. 1201 . https://doi.org/10.1051/ro/2018018","raw_type":null}],"best_oa_location":{"id":"doi:10.1051/ro/2018018","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2018018","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2018/04/ro160288.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W182476373","https://openalex.org/W340849822","https://openalex.org/W614375648","https://openalex.org/W1516499296","https://openalex.org/W1563421332","https://openalex.org/W1964956303","https://openalex.org/W1968031037","https://openalex.org/W1990984428","https://openalex.org/W1991005468","https://openalex.org/W1999651652","https://openalex.org/W2001016876","https://openalex.org/W2002301264","https://openalex.org/W2003006769","https://openalex.org/W2003285839","https://openalex.org/W2009054772","https://openalex.org/W2013926956","https://openalex.org/W2019968939","https://openalex.org/W2024925201","https://openalex.org/W2029932115","https://openalex.org/W2030348309","https://openalex.org/W2036602540","https://openalex.org/W2036813613","https://openalex.org/W2040802026","https://openalex.org/W2060942611","https://openalex.org/W2072517761","https://openalex.org/W2085569611","https://openalex.org/W2089908429","https://openalex.org/W2097336488","https://openalex.org/W2097607403","https://openalex.org/W2101431131","https://openalex.org/W2117502083","https://openalex.org/W2122235509","https://openalex.org/W2171463321","https://openalex.org/W2172291161","https://openalex.org/W2233907134","https://openalex.org/W2269866355","https://openalex.org/W2316622285","https://openalex.org/W2602972600","https://openalex.org/W2787523326","https://openalex.org/W3125705824","https://openalex.org/W4234534407","https://openalex.org/W4246883249"],"related_works":["https://openalex.org/W2361363208","https://openalex.org/W2352947988","https://openalex.org/W2035934944","https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W2365714836","https://openalex.org/W2368445280","https://openalex.org/W2969580250","https://openalex.org/W2182351413","https://openalex.org/W4213342932"],"abstract_inverted_index":{"Multi-objective":[0],"programming":[1,58],"became":[2],"more":[3,5],"and":[4,20,37,82,105],"popular":[6],"in":[7,13,23],"real":[8],"world":[9],"decision":[10],"making":[11],"problems":[12],"recent":[14],"decades.":[15],"There":[16],"is":[17,47,99],"an":[18],"underlying":[19],"fundamental":[21],"uncertainty":[22],"almost":[24],"all":[25],"of":[26,32,54,65,78,95],"these":[27],"problems.":[28],"Among":[29],"different":[30,111],"frameworks":[31],"dealing":[33],"with":[34,88,110],"uncertainty,":[35],"probability":[36],"statistic-based":[38],"schemes":[39],"are":[40,108,119],"well-known.":[41],"In":[42],"this":[43],"paper,":[44],"a":[45,55,63,72,89],"method":[46,61,98],"developed":[48],"to":[49,71],"find":[50],"some":[51],"efficient":[52],"solutions":[53],"multi-objective":[56,69],"stochastic":[57,68],"problem.":[59],"The":[60],"composed":[62],"process":[64],"transforming":[66],"the":[67,76,85,96,106,117],"problem":[70,87],"bi-objective":[73],"equivalent":[74],"using":[75],"concept":[77],"Chebyshev":[79],"inequality":[80],"bounds":[81],"then":[83],"solving":[84],"obtained":[86],"fuzzy":[90],"set":[91],"based":[92],"approach.":[93],"Application":[94],"proposed":[97],"examined":[100],"on":[101],"two":[102],"numerical":[103],"examples":[104],"results":[107,118],"compared":[109],"methods.":[112],"These":[113],"comparisons":[114],"illustrated":[115],"that":[116],"satisfying.":[120]},"counts_by_year":[{"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":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}