{"id":"https://openalex.org/W3087183202","doi":"https://doi.org/10.3390/sym12091548","title":"Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations","display_name":"Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations","publication_year":2020,"publication_date":"2020-09-19","ids":{"openalex":"https://openalex.org/W3087183202","doi":"https://doi.org/10.3390/sym12091548","mag":"3087183202"},"language":"en","primary_location":{"id":"doi:10.3390/sym12091548","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091548","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1548/pdf?version=1600770443","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/2073-8994/12/9/1548/pdf?version=1600770443","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029063657","display_name":"Abdul Razzaq Abdul Ghaffar","orcid":"https://orcid.org/0000-0003-4172-9511"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdul Razzaq Abdul Ghaffar","raw_affiliation_strings":["Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh-11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4172-9511","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh-11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029840184","display_name":"Md. Gulzarul Hasan","orcid":"https://orcid.org/0000-0001-6060-0348"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Md. Gulzarul Hasan","raw_affiliation_strings":["Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle-517325, India"],"raw_orcid":"https://orcid.org/0000-0001-6060-0348","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle-517325, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081005098","display_name":"Zubair Ashraf","orcid":"https://orcid.org/0000-0001-7122-2856"},"institutions":[{"id":"https://openalex.org/I90425906","display_name":"South Asian University","ror":"https://ror.org/02kjyst95","country_code":"IN","type":"education","lineage":["https://openalex.org/I90425906"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Zubair Ashraf","raw_affiliation_strings":["Department of Computer Science, South Asian University, New Delhi-110021, India"],"raw_orcid":"https://orcid.org/0000-0001-7122-2856","affiliations":[{"raw_affiliation_string":"Department of Computer Science, South Asian University, New Delhi-110021, India","institution_ids":["https://openalex.org/I90425906"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066920839","display_name":"Mohammad Faisal Khan","orcid":"https://orcid.org/0000-0001-5053-5028"},"institutions":[{"id":"https://openalex.org/I120238654","display_name":"Saudi Electronic University","ror":"https://ror.org/05ndh7v49","country_code":"SA","type":"education","lineage":["https://openalex.org/I120238654"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammad Faisal Khan","raw_affiliation_strings":["College of Science and Theoretical studies, Saudi Electronic University, Riyadh-11673, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5053-5028","affiliations":[{"raw_affiliation_string":"College of Science and Theoretical studies, Saudi Electronic University, Riyadh-11673, Saudi Arabia","institution_ids":["https://openalex.org/I120238654"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029840184"],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4885,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.82311696,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"12","issue":"9","first_page":"1548","last_page":"1548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9998999834060669,"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":0.9998999834060669,"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":0.963100016117096,"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":0.947700023651123,"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/preference","display_name":"Preference","score":0.6430583000183105},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.586084246635437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5724396705627441},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4650980234146118},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.4556177258491516},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4472985565662384},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4277503490447998},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.42235898971557617},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4193474352359772},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.41897523403167725},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.37561118602752686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36678531765937805},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3267827332019806},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12418115139007568}],"concepts":[{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.6430583000183105},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.586084246635437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5724396705627441},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4650980234146118},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.4556177258491516},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4472985565662384},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4277503490447998},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.42235898971557617},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4193474352359772},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.41897523403167725},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.37561118602752686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36678531765937805},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3267827332019806},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12418115139007568},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12091548","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091548","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1548/pdf?version=1600770443","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:916c688c509840d4b0fd36975891c199","is_oa":true,"landing_page_url":"https://doaj.org/article/916c688c509840d4b0fd36975891c199","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":"Symmetry, Vol 12, Iss 9, p 1548 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/9/1548/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12091548","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/sym12091548","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12091548","pdf_url":"https://www.mdpi.com/2073-8994/12/9/1548/pdf?version=1600770443","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":[{"id":"https://metadata.un.org/sdg/16","score":0.44999998807907104,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W7287913","https://openalex.org/W1489517264","https://openalex.org/W1509095035","https://openalex.org/W1579101628","https://openalex.org/W1608124083","https://openalex.org/W1964166152","https://openalex.org/W1971792895","https://openalex.org/W1974371235","https://openalex.org/W1980564456","https://openalex.org/W1987782587","https://openalex.org/W1988131669","https://openalex.org/W1997188340","https://openalex.org/W2000191646","https://openalex.org/W2009157835","https://openalex.org/W2009775354","https://openalex.org/W2012405004","https://openalex.org/W2018278688","https://openalex.org/W2025657172","https://openalex.org/W2025736455","https://openalex.org/W2029148771","https://openalex.org/W2030978108","https://openalex.org/W2035812476","https://openalex.org/W2044754621","https://openalex.org/W2046086733","https://openalex.org/W2055475880","https://openalex.org/W2057314357","https://openalex.org/W2068569787","https://openalex.org/W2069109824","https://openalex.org/W2076367038","https://openalex.org/W2076994513","https://openalex.org/W2084649290","https://openalex.org/W2091955979","https://openalex.org/W2106292145","https://openalex.org/W2123433322","https://openalex.org/W2148857004","https://openalex.org/W2152358062","https://openalex.org/W2158550687","https://openalex.org/W2171715801","https://openalex.org/W2191676128","https://openalex.org/W2219221861","https://openalex.org/W2316533599","https://openalex.org/W2406449110","https://openalex.org/W2479656199","https://openalex.org/W2490197496","https://openalex.org/W2549221612","https://openalex.org/W2587275123","https://openalex.org/W2613585842","https://openalex.org/W2619248892","https://openalex.org/W2733931363","https://openalex.org/W2770794383","https://openalex.org/W2775477309","https://openalex.org/W2793733838","https://openalex.org/W2810462588","https://openalex.org/W2897221596","https://openalex.org/W2906967888","https://openalex.org/W2907940794","https://openalex.org/W2911745200","https://openalex.org/W2912565176","https://openalex.org/W2914156675","https://openalex.org/W2927676735","https://openalex.org/W2929104326","https://openalex.org/W2931420211","https://openalex.org/W2944323565","https://openalex.org/W2949693766","https://openalex.org/W2964131411","https://openalex.org/W3034148383","https://openalex.org/W3105415258","https://openalex.org/W4211007335","https://openalex.org/W4289254296","https://openalex.org/W4292158025","https://openalex.org/W6643966432","https://openalex.org/W6662110255","https://openalex.org/W6740591119","https://openalex.org/W6747262802","https://openalex.org/W6760795807","https://openalex.org/W6761290979"],"related_works":["https://openalex.org/W4206081075","https://openalex.org/W2253053392","https://openalex.org/W2116249946","https://openalex.org/W2781808531","https://openalex.org/W1486684451","https://openalex.org/W2674573885","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W22698454","https://openalex.org/W2573957424"],"abstract_inverted_index":{"Fuzzy":[0],"goal":[1,68,79,112],"programming":[2,113],"(FGP)":[3],"is":[4,70,121,213,256],"applied":[5,257],"to":[6,49,82,102,185,258],"solve":[7],"fuzzy":[8,19,31,94,111,116,145,157,176,195],"multi-objective":[9],"optimization":[10],"problems.":[11],"In":[12,123],"FGP,":[13],"the":[14,22,27,30,42,54,60,83,89,124,135,139,150,156,164,174,189,210,217,222,230,260,269,285,290,298,301,308],"weights":[15],"are":[16,45,57,97,225],"associated":[17,87],"with":[18,51,88,114,193,237],"goals":[20,32],"for":[21,173,284,297],"preference":[23,43,55,91,117,177],"among":[24,155],"them.":[25,104],"However,":[26],"hierarchy":[28],"within":[29],"depends":[33],"on":[34],"several":[35],"uncertain":[36],"criteria,":[37],"decided":[38],"by":[39,59],"experts,":[40],"so":[41],"relations":[44,56,118,178],"not":[46],"always":[47],"easy":[48],"associate":[50],"weight.":[52],"Therefore,":[53],"provided":[58],"decision-makers":[61],"in":[62,106,314],"terms":[63],"of":[64,138,141,144,149,153,229,241,262,268],"linguistic":[65,90],"relationships,":[66],"i.e.,":[67],"A":[69,180,251],"slightly":[71],"or":[72,74],"moderately":[73],"significantly":[75],"more":[76],"important":[77],"than":[78],"B.":[80],"Due":[81],"vagueness":[84],"and":[85,100,147,166,170,187,198,201,221,245,275,307],"ambiguity":[86],"relations,":[92],"intuitionistic":[93,115,175,194],"sets":[95],"(IFSs)":[96],"most":[98],"efficient":[99,276],"suitable":[101],"handle":[103],"Thus,":[105],"this":[107],"paper,":[108],"a":[109,242,246,273],"new":[110],"(FGP-IFPR)":[119],"approach":[120,212],"proposed.":[122],"proposed":[125,231,263],"FGP-IFPR":[126,191,208,232,292,303,310],"model,":[127],"an":[128,160,238],"achievement":[129],"function":[130,152,271],"has":[131,182,280],"been":[132,183,235,281],"developed":[133,214,253],"via":[134],"convex":[136],"combination":[137],"sum":[140],"individual":[142],"grades":[143],"objectives":[146],"amount":[148],"score":[151],"IFPRs":[154],"goals.":[158],"As":[159],"extension,":[161],"we":[162],"presented":[163,236],"linear":[165,309],"non-linear,":[167],"namely,":[168],"exponential":[169,291],"hyperbolic":[171,199,302],"functions":[172],"(IFPRs).":[179],"study":[181],"made":[184],"compare":[186,259],"analyze":[188],"three":[190,207],"models":[192,233],"linear,":[196],"exponential,":[197],"membership":[200],"non-membership":[202],"functions.":[203],"For":[204],"solving":[205],"all":[206],"models,":[209],"solution":[211,224],"that":[215,283],"established":[216],"corresponding":[218],"crisp":[219],"formulations,":[220],"optimal":[223],"obtained.":[226],"The":[227,265],"validations":[228],"have":[234],"experimental":[239],"investigation":[240],"numerical":[243],"problem":[244,288],"banking":[247],"financial":[248],"statement":[249],"problem.":[250],"newly":[252],"distance":[254,270],"measure":[255],"efficiency":[261],"models.":[264],"minimum":[266],"value":[267],"represents":[272],"better":[274],"model.":[277],"Finally,":[278],"it":[279],"found":[282],"first":[286],"illustrative":[287],"considered,":[289],"model":[293,304,311],"performs":[294,305],"best,":[295],"whereas":[296],"second":[299],"problem,":[300],"best":[306],"shows":[312],"worst":[313],"both":[315],"cases.":[316]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
