{"id":"https://openalex.org/W4294068579","doi":"https://doi.org/10.1109/access.2022.3203717","title":"Einstein Ordered Weighted Aggregation Operators for Pythagorean Fuzzy Hypersoft Set With Its Application to Solve MCDM Problem","display_name":"Einstein Ordered Weighted Aggregation Operators for Pythagorean Fuzzy Hypersoft Set With Its Application to Solve MCDM Problem","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4294068579","doi":"https://doi.org/10.1109/access.2022.3203717"},"language":"en","primary_location":{"id":"doi:10.1109/access.2022.3203717","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3203717","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.2022.3203717","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/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]},{"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":["CN","PK"],"is_corresponding":true,"raw_author_name":"Rana Muhammad Zulqarnain","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, China","Department of Mathematics, University of Management and Technology Sialkot, Sialkot, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-2656-8679","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology Sialkot, Sialkot, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"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/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/A5057488732","display_name":"Hanen Karamti","orcid":"https://orcid.org/0000-0001-5162-2692"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hanen Karamti","raw_affiliation_strings":["Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004567134","display_name":"Dariusz Grzelczyk","orcid":"https://orcid.org/0000-0002-7638-6582"},"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":"Dariusz Grzelczyk","raw_affiliation_strings":["Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland"],"raw_orcid":null,"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/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":"https://orcid.org/0000-0002-0475-3320","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Thailand","institution_ids":["https://openalex.org/I4210090662"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087152064","display_name":"Muhammad Asif","orcid":"https://orcid.org/0000-0001-5684-4737"},"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":"Muhammad Asif","raw_affiliation_strings":["Department of Mathematics, University of Management and Technology Sialkot, Sialkot, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-5684-4737","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology Sialkot, Sialkot, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5080364045"],"corresponding_institution_ids":["https://openalex.org/I135237710","https://openalex.org/I87482320"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.5469,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.93188964,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":null,"first_page":"95294","last_page":"95320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9976000189781189,"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":0.9976000189781189,"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":0.9973999857902527,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.932699978351593,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.9493066668510437},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.581403374671936},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5462729930877686},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5067737698554993},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4889139235019684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44844183325767517},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.4229722023010254},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3675462603569031},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34149008989334106}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9493066668510437},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.581403374671936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5462729930877686},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5067737698554993},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4889139235019684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44844183325767517},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.4229722023010254},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3675462603569031},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34149008989334106},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2022.3203717","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3203717","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:b3dc97b5b1924f2ea019c9572e9fbbe3","is_oa":true,"landing_page_url":"https://doaj.org/article/b3dc97b5b1924f2ea019c9572e9fbbe3","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 95294-95320 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2022.3203717","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3203717","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":[{"score":0.7300000190734863,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G4879914989","display_name":null,"funder_award_id":"R.G.P. 1/169/43","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"},{"id":"https://openalex.org/G5638695643","display_name":null,"funder_award_id":"PNURSP2022R192","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"},{"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":61,"referenced_works":["https://openalex.org/W1542837303","https://openalex.org/W1647667069","https://openalex.org/W1829951598","https://openalex.org/W1965777053","https://openalex.org/W1971875039","https://openalex.org/W1978352585","https://openalex.org/W1980564456","https://openalex.org/W1987729209","https://openalex.org/W1989832241","https://openalex.org/W1990975338","https://openalex.org/W2013932252","https://openalex.org/W2068402605","https://openalex.org/W2069754181","https://openalex.org/W2083141276","https://openalex.org/W2083267403","https://openalex.org/W2208115510","https://openalex.org/W2311142332","https://openalex.org/W2335835212","https://openalex.org/W2374072881","https://openalex.org/W2550247067","https://openalex.org/W2611273622","https://openalex.org/W2769278513","https://openalex.org/W2769759034","https://openalex.org/W2792203469","https://openalex.org/W2934195809","https://openalex.org/W2951758213","https://openalex.org/W2955609129","https://openalex.org/W2974508190","https://openalex.org/W2980905588","https://openalex.org/W2988347501","https://openalex.org/W3004156516","https://openalex.org/W3038331152","https://openalex.org/W3047313007","https://openalex.org/W3118350556","https://openalex.org/W3127056016","https://openalex.org/W3128354297","https://openalex.org/W3130055004","https://openalex.org/W3136052643","https://openalex.org/W3165394922","https://openalex.org/W3176039420","https://openalex.org/W3185649761","https://openalex.org/W3199559778","https://openalex.org/W3215047300","https://openalex.org/W4205837102","https://openalex.org/W4211007335","https://openalex.org/W4213045795","https://openalex.org/W4214824237","https://openalex.org/W4220671272","https://openalex.org/W4229377446","https://openalex.org/W4233196928","https://openalex.org/W4283774121","https://openalex.org/W4285733257","https://openalex.org/W4287326183","https://openalex.org/W4366998981","https://openalex.org/W6693091319","https://openalex.org/W6746607324","https://openalex.org/W6749324043","https://openalex.org/W6772921870","https://openalex.org/W6780026933","https://openalex.org/W6840287700","https://openalex.org/W6851728330"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4210969441","https://openalex.org/W4313271080","https://openalex.org/W4378767041","https://openalex.org/W2050612014","https://openalex.org/W3166167233","https://openalex.org/W2387128994","https://openalex.org/W3093594498","https://openalex.org/W2894968817"],"abstract_inverted_index":{"The":[0,49,193,259],"Pythagorean":[1,12,53,86,102,132,155,162,278],"fuzzy":[2,13,54,66,87,103,133,156,163,279],"hypersoft":[3,57,88,104,134,157,164,280],"set":[4,15,105,135],"is":[5,117,175,209,223,266],"the":[6,11,24,28,39,79,85,101,131,227,235,249,263,277],"most":[7,250],"generalized":[8],"form":[9,51],"of":[10,52,141,186,217],"soft":[14],"used":[16],"to":[17,109,180,200,205,225,254],"resolve":[18],"indeterminate":[19],"and":[20,43,68,95,112,161,231,269],"inexplicit":[21],"information":[22,274],"in":[23,37,65,74,106,125,139,177,220,271],"decision-making":[25,114,174,188,218,242,257],"procedure,":[26],"considering":[27,38],"parameters\u2019":[29],"multi-sub-attributes.":[30],"Aggregation":[31],"operators":[32,83,148,168],"execute":[33],"a":[34,62,71,239],"dynamic":[35],"role":[36],"two":[40],"prospect":[41],"sequences":[42],"eliminating":[44],"anxieties":[45],"from":[46],"this":[47],"perception.":[48],"hybrid":[50],"sets":[55,58],"with":[56,93,169],"has":[59,244],"appeared":[60],"as":[61,70],"supportive":[63],"structure":[64],"mathematics":[67],"ensued":[69],"convenient":[72],"perspective":[73],"decision-making.":[75,126],"This":[76],"paper":[77],"prolongs":[78],"Einstein-weighted":[80],"ordered":[81],"aggregation":[82,147,237],"for":[84,121,130,212],"set,":[89],"which":[90,208,247],"proficiently":[91],"contracts":[92],"tentative":[94],"confusing":[96],"data.":[97],"Experts":[98],"are":[99],"using":[100],"their":[107,170],"quest":[108],"report":[110],"indefinite":[111],"specific":[113],"processes.":[115],"It":[116],"an":[118],"effective":[119,268],"technique":[120],"enlarging":[122],"unsure":[123],"facts":[124],"Some":[127],"operational":[128,153],"laws":[129],"have":[136],"been":[137,245],"projected":[138],"light":[140],"Einstein\u2019s":[142],"operations.":[143],"Two":[144],"innovative":[145],"Einstein-ordered":[146,158,165],"were":[149],"established":[150,228],"based":[151,275],"on":[152,234,276],"laws:":[154],"weighted":[159,166],"average":[160],"geometric":[167],"essential":[171],"properties.":[172],"Multi-criteria":[173],"imperative":[176],"overcoming":[178],"barriers":[179],"real-world":[181],"complications.":[182],"However,":[183],"conventional":[184],"methods":[185],"multi-criteria":[187,241,256],"regularly":[189],"provide":[190],"inconsistent":[191],"results.":[192],"extended":[194],"model":[195],"appraisals":[196],"recognized":[197],"score":[198],"values":[199],"regulate":[201],"robotic":[202],"agri-farming":[203],"equated":[204],"prevalent":[206],"methods,":[207],"more":[210,267],"useful":[211],"agribusiness.":[213],"A":[214],"numerical":[215],"illustration":[216],"complications":[219],"real-life":[221],"farming":[222],"deliberated":[224],"authenticate":[226],"method\u2019s":[229],"supremacy":[230],"applicability.":[232],"Based":[233],"anticipated":[236],"operators,":[238],"robust":[240],"method":[243],"presented,":[246],"delivers":[248],"appropriate":[251],"outcomes":[252],"compared":[253],"existing":[255],"techniques.":[258],"consequences":[260],"show":[261],"that":[262],"intended":[264],"approach":[265],"stable":[270],"handling":[272],"rough":[273],"set.":[281]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
