{"id":"https://openalex.org/W3208067371","doi":"https://doi.org/10.3390/sym13112010","title":"Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making","display_name":"Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making","publication_year":2021,"publication_date":"2021-10-23","ids":{"openalex":"https://openalex.org/W3208067371","doi":"https://doi.org/10.3390/sym13112010","mag":"3208067371"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112010","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112010","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2010/pdf?version=1635910276","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/2073-8994/13/11/2010/pdf?version=1635910276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014456358","display_name":"Muhammad Bilal","orcid":"https://orcid.org/0000-0002-6788-0909"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Asim Bilal","raw_affiliation_strings":["Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078902055","display_name":"Muhammad Shabir","orcid":"https://orcid.org/0000-0002-3161-8482"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shabir","raw_affiliation_strings":["Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009981956","display_name":"Ahmad N. Al\u2010Kenani","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad N. Al-Kenani","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5559-5951","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014456358"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.434,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.82799468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"11","first_page":"2010","last_page":"2010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9970999956130981,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9871000051498413,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.5932767987251282},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.5666366219520569},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5565593838691711},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5540390610694885},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5152969360351562},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5051730275154114},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4189074635505676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36331549286842346},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3474983870983124},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30552026629447937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.236761212348938}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5932767987251282},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.5666366219520569},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5565593838691711},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5540390610694885},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5152969360351562},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5051730275154114},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4189074635505676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36331549286842346},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3474983870983124},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30552026629447937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.236761212348938}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13112010","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112010","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2010/pdf?version=1635910276","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:6528eb990860432fbcb788e7486d0174","is_oa":true,"landing_page_url":"https://doaj.org/article/6528eb990860432fbcb788e7486d0174","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 13, Iss 11, p 2010 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2010/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112010","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/sym13112010","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112010","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2010/pdf?version=1635910276","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":"Peace, Justice and strong institutions","score":0.800000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208067371.pdf","grobid_xml":"https://content.openalex.org/works/W3208067371.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W881110586","https://openalex.org/W1969463949","https://openalex.org/W1985326909","https://openalex.org/W2002367458","https://openalex.org/W2002541167","https://openalex.org/W2009653394","https://openalex.org/W2013932252","https://openalex.org/W2027654459","https://openalex.org/W2031345712","https://openalex.org/W2042796353","https://openalex.org/W2093456061","https://openalex.org/W2514754342","https://openalex.org/W2536602045","https://openalex.org/W2574780438","https://openalex.org/W2587709158","https://openalex.org/W2724404692","https://openalex.org/W2746747652","https://openalex.org/W2756292711","https://openalex.org/W2789682920","https://openalex.org/W2807924617","https://openalex.org/W2808872784","https://openalex.org/W2884166416","https://openalex.org/W2884892695","https://openalex.org/W2935807176","https://openalex.org/W2953822493","https://openalex.org/W2997198052","https://openalex.org/W3030129408","https://openalex.org/W3101994482","https://openalex.org/W3136750270","https://openalex.org/W3153347785","https://openalex.org/W3172451173","https://openalex.org/W4211007335","https://openalex.org/W4255833381","https://openalex.org/W4292295629","https://openalex.org/W6600344144","https://openalex.org/W6728659305"],"related_works":["https://openalex.org/W3038608274","https://openalex.org/W1990851617","https://openalex.org/W3013738389","https://openalex.org/W2121560876","https://openalex.org/W2253053392","https://openalex.org/W2184441312","https://openalex.org/W4206081075","https://openalex.org/W1486684451","https://openalex.org/W4361984403","https://openalex.org/W4361273540"],"abstract_inverted_index":{"Yager":[0],"recently":[1],"introduced":[2,150],"the":[3,51,69,109,120,138,153,156,161,186,198,208,213,221,231,234,245,257],"q-rung":[4,40,62,73,83,97,142,173],"orthopair":[5,41,63,74,84,98,143,174],"fuzzy":[6,42,64,75,85,99,127,134,144,175],"set":[7,65,100],"to":[8,50,66,151,255],"accommodate":[9],"uncertainty":[10],"in":[11,24,259],"decision-making":[12],"problems.":[13],"A":[14],"binary":[15,46],"relation":[16],"over":[17,101],"dual":[18,102],"universes":[19,103],"has":[20],"a":[21,61,72,95,124,146,189,224,241,260],"vital":[22],"role":[23],"mathematics":[25],"and":[26,36,53,77,219,239],"information":[27],"sciences.":[28],"During":[29],"this":[30,211],"work,":[31],"we":[32,78],"defined":[33,79],"upper":[34],"approximations":[35,38],"lower":[37],"of":[39,60,71,82,94,123,141,155,163,188,226,233,237,247],"sets":[43,176],"using":[44,137],"crisp":[45],"relations":[47],"with":[48,185],"regard":[49],"aftersets":[52],"foresets.":[54],"We":[55],"used":[56],"an":[57,181,250],"accuracy":[58,70],"measure":[59],"search":[67],"out":[68],"set,":[76,128],"two":[80,112],"types":[81],"topologies":[86],"induced":[87],"by":[88],"reflexive":[89],"relations.":[90],"The":[91,202],"novel":[92],"concept":[93],"rough":[96,125,132],"is":[104,183,205,216],"more":[105,114,200],"flexible":[106],"when":[107,180],"debating":[108],"symmetry":[110,154,187,232],"between":[111],"or":[113],"objects":[115],"that":[116],"are":[117],"better":[118],"than":[119],"prevailing":[121],"notion":[122],"Pythagorean":[126],"as":[129,131],"well":[130],"intuitionistic":[133],"sets.":[135],"Furthermore,":[136],"score":[139],"function":[140],"sets,":[145],"practical":[147],"approach":[148,196,204],"was":[149],"research":[152],"optimal":[157],"decision":[158,168],"and,":[159],"therefore,":[160],"ranking":[162,218,246],"feasible":[164,227],"alternatives.":[165],"Multiple":[166],"criteria":[167],"making":[169],"(MCDM)":[170],"methods":[171],"for":[172,230,249],"cannot":[177],"solve":[178],"problems":[179],"individual":[182],"faced":[184],"two-sided":[190,235],"matching":[191,236],"MCDM":[192],"problem.":[193],"This":[194],"new":[195,206],"solves":[197],"matter":[199],"accurately.":[201],"devised":[203],"within":[207],"literature.":[209],"In":[210],"method,":[212],"main":[214],"focus":[215],"on":[217,244],"selecting":[220],"alternative":[222],"from":[223],"collection":[225],"alternatives,":[228,238],"reckoning":[229],"providing":[240],"solution":[242],"based":[243],"alternatives":[248],"issue":[251],"containing":[252],"conflicting":[253],"criteria,":[254],"assist":[256],"decision-maker":[258],"final":[261],"decision.":[262]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2021-11-08T00:00:00"}
