{"id":"https://openalex.org/W4285163445","doi":"https://doi.org/10.37190/ord220103","title":"An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers","display_name":"An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4285163445","doi":"https://doi.org/10.37190/ord220103"},"language":"en","primary_location":{"id":"doi:10.37190/ord220103","is_oa":true,"landing_page_url":"https://doi.org/10.37190/ord220103","pdf_url":"https://doi.org/10.37190/ord220103","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37190/ord220103","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012563758","display_name":"Vandana Goyal","orcid":"https://orcid.org/0009-0007-2080-7687"},"institutions":[{"id":"https://openalex.org/I155284866","display_name":"Maharishi Markandeshwar University, Mullana","ror":"https://ror.org/013qfkw58","country_code":"IN","type":"education","lineage":["https://openalex.org/I155284866"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vandana Goyal","raw_affiliation_strings":["Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India","institution_ids":["https://openalex.org/I155284866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044829821","display_name":"Namrata Rani","orcid":"https://orcid.org/0000-0001-8020-0915"},"institutions":[{"id":"https://openalex.org/I155284866","display_name":"Maharishi Markandeshwar University, Mullana","ror":"https://ror.org/013qfkw58","country_code":"IN","type":"education","lineage":["https://openalex.org/I155284866"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Namrata Rani","raw_affiliation_strings":["Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India","institution_ids":["https://openalex.org/I155284866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034853815","display_name":"Deepak Gupta","orcid":"https://orcid.org/0000-0002-3019-7161"},"institutions":[{"id":"https://openalex.org/I155284866","display_name":"Maharishi Markandeshwar University, Mullana","ror":"https://ror.org/013qfkw58","country_code":"IN","type":"education","lineage":["https://openalex.org/I155284866"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Deepak Gupta","raw_affiliation_strings":["Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Maharishi Markandeshwar, Mullana-Ambala, India","institution_ids":["https://openalex.org/I155284866"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034853815"],"corresponding_institution_ids":["https://openalex.org/I155284866"],"apc_list":null,"apc_paid":null,"fwci":0.0992,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.35698124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"32","issue":"1","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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9926000237464905,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.989799976348877,"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/mathematics","display_name":"Mathematics","score":0.7040992975234985},{"id":"https://openalex.org/keywords/flowchart","display_name":"Flowchart","score":0.658962070941925},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.639640212059021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6207464337348938},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.5817686319351196},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5480676889419556},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5117430686950684},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5018446445465088},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4897775650024414},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46231609582901},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4497032165527344},{"id":"https://openalex.org/keywords/parametric-programming","display_name":"Parametric programming","score":0.424270361661911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26263752579689026},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.21149027347564697},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08032265305519104},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0676957368850708}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7040992975234985},{"id":"https://openalex.org/C72041958","wikidata":"https://www.wikidata.org/wiki/Q185092","display_name":"Flowchart","level":2,"score":0.658962070941925},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.639640212059021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6207464337348938},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.5817686319351196},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5480676889419556},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5117430686950684},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5018446445465088},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4897775650024414},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46231609582901},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4497032165527344},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.424270361661911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26263752579689026},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.21149027347564697},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08032265305519104},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0676957368850708},{"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},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":4,"locations":[{"id":"doi:10.37190/ord220103","is_oa":true,"landing_page_url":"https://doi.org/10.37190/ord220103","pdf_url":"https://doi.org/10.37190/ord220103","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wut:journl:v:32:y:2022:i:1:p:49-71:id:2620","is_oa":false,"landing_page_url":"https://ord.pwr.edu.pl/assets/papers_archive/2620%20-%20published.pdf","pdf_url":"https://ord.pwr.edu.pl/assets/papers_archive/2620%20-%20published.pdf","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"},{"id":"pmh:oai:dbc.wroc.pl:145434","is_oa":true,"landing_page_url":"https://dbc.wroc.pl/dlibra/publication/184509/edition/145434/content","pdf_url":"https://dbc.wroc.pl/Content/145434/03.pdf","source":{"id":"https://openalex.org/S4210167977","display_name":"Prace Naukowe Uniwersytetu Ekonomicznego we Wroc\u0142awiu","issn_l":"1899-3192","issn":["1899-3192","2392-0041"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4322697539","host_organization_name":"Wroclaw University of Economics","host_organization_lineage":["https://openalex.org/P4322697539"],"host_organization_lineage_names":["Wroclaw University of Economics"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Politechnika Wroc\u0142awska","raw_type":"artyku\u0142"},{"id":"pmh:oai:doaj.org/article:7591bc0b8b9948f1a1dd9ed31f2f0687","is_oa":true,"landing_page_url":"https://doaj.org/article/7591bc0b8b9948f1a1dd9ed31f2f0687","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Operations Research and Decisions, Vol vol. 32, Iss no. 1, Pp 49-71 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.37190/ord220103","is_oa":true,"landing_page_url":"https://doi.org/10.37190/ord220103","pdf_url":"https://doi.org/10.37190/ord220103","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285163445.pdf","grobid_xml":"https://content.openalex.org/works/W4285163445.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W90712649","https://openalex.org/W128994219","https://openalex.org/W1521551902","https://openalex.org/W1966757346","https://openalex.org/W1967956032","https://openalex.org/W2026518456","https://openalex.org/W2035511890","https://openalex.org/W2047817929","https://openalex.org/W2066261348","https://openalex.org/W2110311953","https://openalex.org/W2138353895","https://openalex.org/W2156577211","https://openalex.org/W2326200453","https://openalex.org/W2471811767","https://openalex.org/W2605016500","https://openalex.org/W2747260246","https://openalex.org/W2766765374","https://openalex.org/W2771233855","https://openalex.org/W2807637204","https://openalex.org/W2910935027","https://openalex.org/W2914519071","https://openalex.org/W2914895754","https://openalex.org/W2938240794","https://openalex.org/W2990538730","https://openalex.org/W3091965925","https://openalex.org/W3103531667","https://openalex.org/W3120242536","https://openalex.org/W3123344192","https://openalex.org/W3125233672","https://openalex.org/W3144576744","https://openalex.org/W3175530102","https://openalex.org/W3179725126","https://openalex.org/W3184332097","https://openalex.org/W3198471014","https://openalex.org/W3198948233","https://openalex.org/W3200639542","https://openalex.org/W3203684830","https://openalex.org/W3205921221","https://openalex.org/W4230588984","https://openalex.org/W4251323539","https://openalex.org/W4254172795","https://openalex.org/W4313498479","https://openalex.org/W6600340491","https://openalex.org/W6602390520","https://openalex.org/W6603037545","https://openalex.org/W6840081490"],"related_works":["https://openalex.org/W2112847829","https://openalex.org/W4293088966","https://openalex.org/W4297407962","https://openalex.org/W1878408459","https://openalex.org/W2753327353","https://openalex.org/W4297797735","https://openalex.org/W1496670269","https://openalex.org/W3120242536","https://openalex.org/W3179725126","https://openalex.org/W2073468500"],"abstract_inverted_index":{"This":[0,105],"study":[1],"proposes":[2],"a":[3,11,61,73,94,97,127,134],"methodology":[4,122],"to":[5,71,92,111,125],"obtain":[6,72,93],"an":[7,78,116],"efficient":[8],"solution":[9],"for":[10],"programming":[12,66],"model":[13,67,75,89,95,107],"which":[14],"is":[15,47,69,90,108,141],"multi-objective":[16,63],"quadratic":[17,64],"fractional":[18,65],"with":[19,96],"pentagonal":[20],"fuzzy":[21],"numbers":[22],"as":[23],"coefficients":[24,46],"in":[25,57],"all":[26],"the":[27,40,45,51,58,83,102,121,131,138],"objective":[28,99],"functions":[29],"and":[30,118],"constraints.":[31],"The":[32],"proposed":[33],"approach":[34,140],"consists":[35],"of":[36,44,54,130],"three":[37],"stages.":[38],"In":[39,82],"first":[41],"stage,":[42,60,85],"defuzzification":[43],"carried":[48],"out":[49],"using":[50],"mean":[52],"method":[53],"\u03b1-cut.":[55],"Then,":[56],"second":[59],"crisp":[62],"(MOQFP)":[68],"constructed":[70],"non-fractional":[74,88],"based":[76],"on":[77],"iterative":[79],"parametric":[80],"approach.":[81,132],"final":[84,106],"this":[86],"multiobjective":[87],"transformed":[91],"single":[98],"by":[100],"applying":[101],"\u03b5-constraint":[103],"method.":[104],"then":[109],"solved":[110],"get":[112],"desired":[113],"solution.":[114],"Also,":[115],"algorithm":[117],"flowchart":[119],"expressing":[120],"are":[123],"given":[124],"present":[126],"clear":[128],"picture":[129],"Finally,":[133],"numerical":[135],"example":[136],"illustrating":[137],"complete":[139],"given.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}