{"id":"https://openalex.org/W4206483368","doi":"https://doi.org/10.3233/jifs-211747","title":"Study on multi-objective nonlinear programming problem with rough parameters","display_name":"Study on multi-objective nonlinear programming problem with rough parameters","publication_year":2021,"publication_date":"2021-12-31","ids":{"openalex":"https://openalex.org/W4206483368","doi":"https://doi.org/10.3233/jifs-211747"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-211747","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-211747","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy 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/A5054194585","display_name":"Harish Garg","orcid":"https://orcid.org/0000-0001-9099-8422"},"institutions":[{"id":"https://openalex.org/I162030827","display_name":"Thapar Institute of Engineering & Technology","ror":"https://ror.org/00wdq3744","country_code":"IN","type":"education","lineage":["https://openalex.org/I162030827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Harish Garg","raw_affiliation_strings":["School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India","institution_ids":["https://openalex.org/I162030827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012460942","display_name":"Sultan S. Alodhaibi","orcid":"https://orcid.org/0000-0003-4439-1878"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sultan S. Alodhaibi","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts, Qassim Univesity, ArRass, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts, Qassim Univesity, ArRass, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050384109","display_name":"Hamiden Abd El\u2010Wahed Khalifa","orcid":"https://orcid.org/0000-0002-8269-8822"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]},{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Hamiden Abd El-Wahed Khalifa","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts, Qassim University, Al-Badayaa, Saudi Arabia","Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University Giza, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badayaa, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]},{"raw_affiliation_string":"Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University Giza, Egypt","institution_ids":["https://openalex.org/I145487455"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054194585"],"corresponding_institution_ids":["https://openalex.org/I162030827"],"apc_list":null,"apc_paid":null,"fwci":0.7238,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75941717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"4","first_page":"3591","last_page":"3604"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.984000027179718,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.97079998254776,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.8977274298667908},{"id":"https://openalex.org/keywords/vagueness","display_name":"Vagueness","score":0.7841523289680481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6395680904388428},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5687803030014038},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5643917918205261},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5151559114456177},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48231935501098633},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4748568534851074},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4685429334640503},{"id":"https://openalex.org/keywords/dominance-based-rough-set-approach","display_name":"Dominance-based rough set approach","score":0.45983925461769104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3285818099975586},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.15867558121681213},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12095490097999573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06915634870529175},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05645725131034851}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.8977274298667908},{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.7841523289680481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6395680904388428},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5687803030014038},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5643917918205261},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5151559114456177},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48231935501098633},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4748568534851074},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4685429334640503},{"id":"https://openalex.org/C39105242","wikidata":"https://www.wikidata.org/wiki/Q5290286","display_name":"Dominance-based rough set approach","level":3,"score":0.45983925461769104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3285818099975586},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.15867558121681213},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12095490097999573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06915634870529175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05645725131034851},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-211747","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-211747","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W169684044","https://openalex.org/W1973299514","https://openalex.org/W2023368625","https://openalex.org/W2077035426","https://openalex.org/W2103186021","https://openalex.org/W2495617274","https://openalex.org/W2575451392","https://openalex.org/W2808301187","https://openalex.org/W2883508226","https://openalex.org/W2905981774","https://openalex.org/W2964537212","https://openalex.org/W3009229047","https://openalex.org/W3042020401","https://openalex.org/W3133842213","https://openalex.org/W3137447225","https://openalex.org/W3147463932","https://openalex.org/W3152716910","https://openalex.org/W3187962393","https://openalex.org/W3202562673","https://openalex.org/W4232953319","https://openalex.org/W6757907044"],"related_works":["https://openalex.org/W2382975841","https://openalex.org/W1484435280","https://openalex.org/W2165634587","https://openalex.org/W2123662875","https://openalex.org/W2074161014","https://openalex.org/W2127410352","https://openalex.org/W2963142056","https://openalex.org/W2068033140","https://openalex.org/W2032560733","https://openalex.org/W4206483368"],"abstract_inverted_index":{"Rough":[0],"set":[1],"theory,":[2],"introduced":[3],"by":[4,19,108,151],"Pawlak":[5],"in":[6,85],"1981,":[7],"is":[8,34,76],"one":[9],"of":[10,21,28,73],"the":[11,16,74,86,98,110,114,141,145,152,156,170,178],"important":[12],"theories":[13],"to":[14,77,130,168],"express":[15],"vagueness":[17],"not":[18],"means":[20],"membership":[22],"but":[23],"employing":[24],"a":[25,29,65,80],"boundary":[26],"region":[27],"set,":[30],"i.e.,":[31],"an":[32],"object":[33],"approximately":[35],"determined":[36,150],"based":[37],"on":[38,51],"some":[39],"knowledge.":[40],"In":[41,139],"our":[42],"real-life,":[43],"there":[44],"exists":[45],"several":[46],"parameters":[47,60,84,94],"which":[48],"impact":[49],"simultaneously":[50],"each":[52,159],"other":[53],"and":[54,61,104,113,118,135,144,154,173],"hence":[55,119],"dealing":[56],"with":[57,79,82,92],"such":[58],"different":[59],"their":[62,121,175],"conflictness":[63],"create":[64],"multi-objective":[66],"nonlinear":[67],"programming":[68],"problem":[69],"(MONLPP).":[70],"The":[71,89,124],"objective":[72,100],"paper":[75],"deal":[78],"MONLPP":[81,91],"rough":[83,93,142,146],"constraint":[87],"set.":[88],"considered":[90,167],"are":[95,128,149,166],"converted":[96],"into":[97],"two-single":[99],"problems":[101,107],"namely,":[102],"lower":[103,134,153],"upper":[105,136,155],"approximate":[106,137],"using":[109],"weighted":[111],"averaging":[112],"\u025b-":[115],"constraints":[116],"methods":[117],"discussed":[120],"efficient":[122,160],"solutions.":[123],"Karush-Kuhn-Tucker\u2019s":[125],"optimality":[126],"conditions":[127],"applied":[129],"solve":[131],"these":[132],"two":[133,163],"problems.":[138],"addition,":[140],"weights":[143],"parameter":[147],"\u025b":[148],"approximations":[157],"corresponding":[158],"solution.":[161],"Finally,":[162],"numerical":[164],"examples":[165],"demonstrate":[169],"stated":[171],"approach":[172],"discuss":[174],"advantages":[176],"over":[177],"existing":[179],"ones.":[180]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}