{"id":"https://openalex.org/W4291805277","doi":"https://doi.org/10.1109/access.2022.3199071","title":"Some Einstein Geometric Aggregation Operators for q-Rung Orthopair Fuzzy Soft Set With Their Application in MCDM","display_name":"Some Einstein Geometric Aggregation Operators for q-Rung Orthopair Fuzzy Soft Set With Their Application in MCDM","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4291805277","doi":"https://doi.org/10.1109/access.2022.3199071"},"language":"en","primary_location":{"id":"doi:10.1109/access.2022.3199071","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3199071","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2022.3199071","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080364045","display_name":"Rana Muhammad Zulqarnain","orcid":"https://orcid.org/0000-0002-2656-8679"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Rana Muhammad Zulqarnain","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology, Sialkot, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-2656-8679","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Sialkot, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071875096","display_name":"Rifaqat Ali","orcid":"https://orcid.org/0000-0002-2605-1119"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Rifaqat Ali","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, Abha, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, Abha, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025074757","display_name":"Jan Awrejcewicz","orcid":"https://orcid.org/0000-0003-0387-921X"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jan Awrejcewicz","raw_affiliation_strings":["Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland"],"raw_orcid":"https://orcid.org/0000-0003-0387-921X","affiliations":[{"raw_affiliation_string":"Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022884973","display_name":"Imran Siddique","orcid":"https://orcid.org/0000-0002-5060-7906"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imran Siddique","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology, Lahore, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085047470","display_name":"Fahd Jarad","orcid":"https://orcid.org/0000-0002-3303-0623"},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I184693016","display_name":"China Medical University","ror":"https://ror.org/00v408z34","country_code":"TW","type":"education","lineage":["https://openalex.org/I184693016"]},{"id":"https://openalex.org/I4210126829","display_name":"China Medical University Hospital","ror":"https://ror.org/0368s4g32","country_code":"TW","type":"healthcare","lineage":["https://openalex.org/I4210126829"]}],"countries":["TR","TW"],"is_corresponding":false,"raw_author_name":"Fahd Jarad","raw_affiliation_strings":["Department of Mathematics, Cankaya University, Etimesgut, Turkey","Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-3303-0623","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cankaya University, Etimesgut, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan","institution_ids":["https://openalex.org/I4210126829","https://openalex.org/I184693016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038069817","display_name":"Aiyared Iampan","orcid":"https://orcid.org/0000-0002-0475-3320"},"institutions":[{"id":"https://openalex.org/I4210090662","display_name":"University of Phayao","ror":"https://ror.org/00a5mh069","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210090662"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Aiyared Iampan","raw_affiliation_strings":["Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Thailand","institution_ids":["https://openalex.org/I4210090662"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5080364045"],"corresponding_institution_ids":["https://openalex.org/I87482320"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":6.0804,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.96913699,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"10","issue":null,"first_page":"88469","last_page":"88494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9988999962806702,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9988999962806702,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9952999949455261,"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":0.9559000134468079,"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/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.585265040397644},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5561345219612122},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5456193685531616},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5423465967178345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5375093817710876},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.49645835161209106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39030927419662476},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3899575471878052},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34474629163742065},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2339542806148529},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06816759705543518}],"concepts":[{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.585265040397644},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5561345219612122},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5456193685531616},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5423465967178345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5375093817710876},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.49645835161209106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39030927419662476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3899575471878052},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34474629163742065},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2339542806148529},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06816759705543518},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2022.3199071","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3199071","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3cc5dc1d828343768be31a4dec8772c7","is_oa":true,"landing_page_url":"https://doaj.org/article/3cc5dc1d828343768be31a4dec8772c7","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":"IEEE Access, Vol 10, Pp 88469-88494 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2022.3199071","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3199071","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7699999809265137}],"awards":[{"id":"https://openalex.org/G1453177686","display_name":null,"funder_award_id":"R.G.P. 2/51/43","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"}],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1829951598","https://openalex.org/W1965777053","https://openalex.org/W1978352585","https://openalex.org/W1980564456","https://openalex.org/W2013932252","https://openalex.org/W2311142332","https://openalex.org/W2374072881","https://openalex.org/W2514754342","https://openalex.org/W2611273622","https://openalex.org/W2746747652","https://openalex.org/W2769278513","https://openalex.org/W2769759034","https://openalex.org/W2938214891","https://openalex.org/W2951762009","https://openalex.org/W2988347501","https://openalex.org/W2995299237","https://openalex.org/W2997846235","https://openalex.org/W2999200782","https://openalex.org/W3004156516","https://openalex.org/W3020996816","https://openalex.org/W3036760384","https://openalex.org/W3044006605","https://openalex.org/W3047313007","https://openalex.org/W3127056016","https://openalex.org/W3128354297","https://openalex.org/W3133330385","https://openalex.org/W3176039420","https://openalex.org/W3185649761","https://openalex.org/W3194487201","https://openalex.org/W3202391949","https://openalex.org/W3204722363","https://openalex.org/W3215047300","https://openalex.org/W4211007335","https://openalex.org/W4213045795","https://openalex.org/W4220671272","https://openalex.org/W4285183082","https://openalex.org/W4293768785","https://openalex.org/W6693091319","https://openalex.org/W6772921870"],"related_works":["https://openalex.org/W2804188782","https://openalex.org/W4220704772","https://openalex.org/W3035952176","https://openalex.org/W3205037567","https://openalex.org/W4313893761","https://openalex.org/W154089963","https://openalex.org/W2101950038","https://openalex.org/W3196060399","https://openalex.org/W4387398124","https://openalex.org/W1780780370"],"abstract_inverted_index":{"q-rung":[0,91,112,143,165,174],"orthopair":[1,11,90,113,144,166,175],"fuzzy":[2,12,22,28,82,92,104,114,126,145,167,176],"soft":[3,23,29,95,117,146,168,177],"sets":[4,24,30,93,96,115,118],"(q-ROFSS)":[5],"is":[6,15,75,136,155,199,227,247,275],"a":[7,52,100,223],"progressive":[8],"form":[9,88],"for":[10,80,142],"sets.":[13],"It":[14,74],"also":[16],"an":[17,122,243],"appropriate":[18],"extension":[19],"of":[20,55,89,111,133,152,192,206,233,255],"intuitionistic":[21],"(IFSS)":[25],"and":[26,46,64,72,106,128,173,190,253],"Pythagorean":[27],"(PFSS).":[31],"The":[32,49,58,86,108,130,149,264],"strict":[33],"prerequisite":[34],"gives":[35],"assessors":[36],"too":[37],"much":[38],"autonomy":[39],"to":[40,68,137,156,229,249],"precise":[41],"their":[42],"opinions":[43],"about":[44],"membership":[45],"non-membership":[47],"values.":[48],"q-ROFSS":[50,59,240],"has":[51,97,119],"wide":[53],"range":[54],"real-life":[56],"presentations.":[57],"capably":[60],"contracts":[61],"with":[62,94,116,203,259],"unreliable":[63],"ambiguous":[65],"data":[66,83],"equated":[67],"the":[69,76,187,193,204,210,220,231,234,239,251,256],"prevailing":[70,235,279],"IFSS":[71],"PFSS.":[73],"most":[77],"powerful":[78],"method":[79,258],"amplifying":[81],"in":[84,103,125,201],"decision-making.":[85,107,129],"hybrid":[87,109],"emerged":[98],"as":[99,121,164],"helpful":[101],"framework":[102],"mathematics":[105,127],"structure":[110],"occurred":[120],"expedient":[123],"context":[124],"fundamental":[131],"impartial":[132],"this":[134,153],"research":[135,154],"propose":[138],"Einstein\u2019s":[139],"operational":[140],"laws":[141],"numbers":[147],"(q-ROFSNs).":[148],"core":[150],"objective":[151],"develop":[157],"some":[158,260],"geometric":[159,171,181],"aggregation":[160],"operators":[161],"(AOs),":[162],"such":[163],"Einstein":[169,178],"weighted":[170,180],"(q-ROFSEWG),":[172],"ordered":[179],"(q-ROFSEOWG)":[182],"operators.":[183],"We":[184],"will":[185],"discuss":[186],"idempotency,":[188],"boundedness,":[189],"homogeneity":[191],"proposed":[194],"AOs.":[195],"Multi-criteria":[196],"decision-making":[197],"(MCDM)":[198],"dynamic":[200],"dealing":[202],"density":[205],"real-world":[207],"complications.":[208],"Still,":[209],"prevalent":[211],"MCDM":[212,225,236],"techniques":[213],"consistently":[214],"deliver":[215],"irreconcilable":[216],"outcomes.":[217],"Based":[218],"on":[219],"presented":[221],"AOs,":[222],"strong":[224],"technique":[226],"deliberate":[228],"accommodate":[230],"flaws":[232],"approaches":[237],"under":[238],"setting.":[241],"Moreover,":[242],"inclusive":[244],"comparative":[245,268],"analysis":[246],"executed":[248],"endorse":[250],"expediency":[252],"usefulness":[254],"suggested":[257],"previously":[261],"existing":[262],"techniques.":[263],"outcomes":[265],"gained":[266],"through":[267],"studies":[269],"spectacle":[270],"that":[271],"our":[272],"established":[273],"approach":[274],"more":[276],"capable":[277],"than":[278],"methodologies.":[280]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}