{"id":"https://openalex.org/W4313401986","doi":"https://doi.org/10.3390/sym15010130","title":"A Novel Approach for Minimizing Processing Times of Three-Stage Flow Shop Scheduling Problems under Fuzziness","display_name":"A Novel Approach for Minimizing Processing Times of Three-Stage Flow Shop Scheduling Problems under Fuzziness","publication_year":2023,"publication_date":"2023-01-02","ids":{"openalex":"https://openalex.org/W4313401986","doi":"https://doi.org/10.3390/sym15010130"},"language":"en","primary_location":{"id":"doi:10.3390/sym15010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010130","pdf_url":"https://www.mdpi.com/2073-8994/15/1/130/pdf?version=1673607603","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/1/130/pdf?version=1673607603","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036523133","display_name":"Alhanouf Alburaikan","orcid":"https://orcid.org/0000-0002-4420-7287"},"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":"Alhanouf Alburaikan","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-4420-7287","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054194585","display_name":"Harish Garg","orcid":"https://orcid.org/0000-0001-9099-8422"},"institutions":[{"id":"https://openalex.org/I146367977","display_name":"Applied Science Private University","ror":"https://ror.org/01ah6nb52","country_code":"JO","type":"education","lineage":["https://openalex.org/I146367977"]},{"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"]},{"id":"https://openalex.org/I60054993","display_name":"Graphic Era University","ror":"https://ror.org/03wqgqd89","country_code":"IN","type":"education","lineage":["https://openalex.org/I60054993"]}],"countries":["IN","JO"],"is_corresponding":true,"raw_author_name":"Harish Garg","raw_affiliation_strings":["Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan","Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, Uttarakhand, India","School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India"],"raw_orcid":"https://orcid.org/0000-0001-9099-8422","affiliations":[{"raw_affiliation_string":"Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan","institution_ids":["https://openalex.org/I146367977"]},{"raw_affiliation_string":"Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, Uttarakhand, India","institution_ids":["https://openalex.org/I60054993"]},{"raw_affiliation_string":"School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, Punjab, India","institution_ids":["https://openalex.org/I162030827"]}]},{"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-Badaya 51951, Saudi Arabia","Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-8269-8822","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]},{"raw_affiliation_string":"Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5054194585"],"corresponding_institution_ids":["https://openalex.org/I146367977","https://openalex.org/I162030827","https://openalex.org/I60054993"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.8579,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74531125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"15","issue":"1","first_page":"130","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10328","display_name":"Supply Chain and Inventory Management","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9908000230789185,"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/computer-science","display_name":"Computer science","score":0.6409040689468384},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6347392201423645},{"id":"https://openalex.org/keywords/flow-shop-scheduling","display_name":"Flow shop scheduling","score":0.6254070401191711},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6027621030807495},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5381508469581604},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5362673401832581},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.4836045801639557},{"id":"https://openalex.org/keywords/renting","display_name":"Renting","score":0.477088063955307},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.47077083587646484},{"id":"https://openalex.org/keywords/idle","display_name":"Idle","score":0.4261242747306824},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.40952515602111816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2846919596195221},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.27516454458236694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15805336833000183},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.10862493515014648}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6409040689468384},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6347392201423645},{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.6254070401191711},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6027621030807495},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5381508469581604},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5362673401832581},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.4836045801639557},{"id":"https://openalex.org/C85502023","wikidata":"https://www.wikidata.org/wiki/Q157171","display_name":"Renting","level":2,"score":0.477088063955307},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.47077083587646484},{"id":"https://openalex.org/C16320812","wikidata":"https://www.wikidata.org/wiki/Q1812200","display_name":"Idle","level":2,"score":0.4261242747306824},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.40952515602111816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2846919596195221},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.27516454458236694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15805336833000183},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.10862493515014648},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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":3,"locations":[{"id":"doi:10.3390/sym15010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010130","pdf_url":"https://www.mdpi.com/2073-8994/15/1/130/pdf?version=1673607603","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ecf757743c5042fba5109f8b54fade04","is_oa":false,"landing_page_url":"https://doaj.org/article/ecf757743c5042fba5109f8b54fade04","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 1, p 130 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/1/130/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15010130","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15010130","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15010130","pdf_url":"https://www.mdpi.com/2073-8994/15/1/130/pdf?version=1673607603","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4313401986.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1532791960","https://openalex.org/W1550995075","https://openalex.org/W1944441789","https://openalex.org/W1970256129","https://openalex.org/W1993720449","https://openalex.org/W2024085737","https://openalex.org/W2135323982","https://openalex.org/W2471237974","https://openalex.org/W2473560920","https://openalex.org/W2510989726","https://openalex.org/W2520364703","https://openalex.org/W2885816989","https://openalex.org/W2914895754","https://openalex.org/W2928160924","https://openalex.org/W2963195111","https://openalex.org/W2963347283","https://openalex.org/W2985052688","https://openalex.org/W3126637969","https://openalex.org/W3134716184","https://openalex.org/W3156146207","https://openalex.org/W3159015436","https://openalex.org/W3198544021","https://openalex.org/W3199052649","https://openalex.org/W3216729967","https://openalex.org/W4211007335","https://openalex.org/W4226300969","https://openalex.org/W4252010473","https://openalex.org/W4281994799","https://openalex.org/W4285106612","https://openalex.org/W4293787041","https://openalex.org/W4312276594","https://openalex.org/W4312573268","https://openalex.org/W6633263474","https://openalex.org/W6644445145","https://openalex.org/W6720434791","https://openalex.org/W6726737809","https://openalex.org/W6760970515","https://openalex.org/W6791757301","https://openalex.org/W6795233563","https://openalex.org/W6848002018","https://openalex.org/W6963793368"],"related_works":["https://openalex.org/W2967782293","https://openalex.org/W2185192838","https://openalex.org/W2069961172","https://openalex.org/W2955323683","https://openalex.org/W1564838499","https://openalex.org/W2559484340","https://openalex.org/W26892725","https://openalex.org/W2165758382","https://openalex.org/W1971939018","https://openalex.org/W3155166764"],"abstract_inverted_index":{"The":[0,20],"purpose":[1],"of":[2,46,58,78,114,145],"this":[3,34],"research":[4],"is":[5,23,83,134,139],"to":[6,67,85,101,130,141,150],"investigate":[7],"a":[8,47,112],"novel":[9],"three-stage":[10],"flow":[11],"shop":[12],"scheduling":[13],"problem":[14],"with":[15],"an":[16],"ambiguous":[17],"processing":[18,120],"time.":[19],"uncertain":[21],"information":[22],"characterized":[24],"by":[25],"Pentagonal":[26,80],"fuzzy":[27,61,81],"numbers.":[28],"To":[29],"solve":[30],"the":[31,44,51,54,59,74,79,87,93,103,107,131,143,146,152],"problem,":[32],"in":[33,71],"paper,":[35],"two":[36,147],"different":[37],"strategies":[38,148],"are":[39,99],"proposed;":[40],"one":[41],"relies":[42],"on":[43,53],"idea":[45],"ranking":[48],"function,":[49],"and":[50,126,149],"other":[52],"close":[55,75],"interval":[56,76],"approximation":[57,77,90],"pentagonal":[60],"number.":[62],"For":[63],"persons":[64],"that":[65],"need":[66],"be":[68,86],"more":[69],"specific":[70],"their":[72],"requirements,":[73],"number":[82],"judged":[84],"best":[88],"appropriate":[89],"interval.":[91],"Regarding":[92],"rental":[94,104,124],"cost":[95,105],"specification,":[96],"these":[97],"methods":[98],"used":[100],"reduce":[102],"for":[106],"concerned":[108],"devices.":[109],"In":[110],"addition,":[111],"comparison":[113],"our":[115],"suggested":[116],"approach\u2019s":[117],"computed":[118],"total":[119,122],"time,":[121],"machine":[123,127],"cost,":[125],"idle":[128],"time":[129],"existing":[132],"approach":[133],"introduced.":[135],"A":[136],"numerical":[137],"example":[138],"shown":[140],"clarify":[142],"benefits":[144],"help":[151],"readers":[153],"understand":[154],"it":[155],"better.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}