{"id":"https://openalex.org/W3047251877","doi":"https://doi.org/10.1142/s1793005720500131","title":"Approaches to Some Induced Einstein Geometric Aggregation Operators Based on Interval-Valued Pythagorean Fuzzy Numbers and Their Application","display_name":"Approaches to Some Induced Einstein Geometric Aggregation Operators Based on Interval-Valued Pythagorean Fuzzy Numbers and Their Application","publication_year":2020,"publication_date":"2020-07-01","ids":{"openalex":"https://openalex.org/W3047251877","doi":"https://doi.org/10.1142/s1793005720500131","mag":"3047251877"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005720500131","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005720500131","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102402405","display_name":"Khaista Rahman","orcid":null},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Khaista Rahman","raw_affiliation_strings":["Department of Mathematics, Hazara University, Mansehra, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hazara University, Mansehra, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102402405"],"corresponding_institution_ids":["https://openalex.org/I263208278"],"apc_list":null,"apc_paid":null,"fwci":0.8976,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77685042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"16","issue":"02","first_page":"211","last_page":"230"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.98580002784729,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.972599983215332,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8930305242538452},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6936142444610596},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5861194133758545},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5766716599464417},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5733163952827454},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5697126388549805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5295456647872925},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.5027098655700684},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.4784829020500183},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4545125961303711},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4531134366989136},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.446607381105423},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.43583351373672485},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4311946928501129},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.41665688157081604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3957652747631073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29229652881622314},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2718501091003418},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24992713332176208},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.14774996042251587},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1441003680229187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07041731476783752}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8930305242538452},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6936142444610596},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5861194133758545},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5766716599464417},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5733163952827454},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5697126388549805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5295456647872925},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.5027098655700684},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.4784829020500183},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4545125961303711},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4531134366989136},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.446607381105423},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.43583351373672485},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4311946928501129},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.41665688157081604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3957652747631073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29229652881622314},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2718501091003418},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24992713332176208},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.14774996042251587},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1441003680229187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07041731476783752},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793005720500131","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005720500131","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"New Mathematics and Natural Computation","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:nmncxx:v:16:y:2020:i:02:n:s1793005720500131","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S1793005720500131","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1488217585","https://openalex.org/W1668569279","https://openalex.org/W1765570948","https://openalex.org/W1829951598","https://openalex.org/W1968642553","https://openalex.org/W1972591478","https://openalex.org/W1980564456","https://openalex.org/W2013932252","https://openalex.org/W2038720791","https://openalex.org/W2057286464","https://openalex.org/W2079457935","https://openalex.org/W2099024403","https://openalex.org/W2104077967","https://openalex.org/W2130104797","https://openalex.org/W2345848912","https://openalex.org/W2391648306","https://openalex.org/W2412590235","https://openalex.org/W2414387118","https://openalex.org/W2549733045","https://openalex.org/W2595406791","https://openalex.org/W2611273622","https://openalex.org/W2753380059","https://openalex.org/W2756768858","https://openalex.org/W2765931357","https://openalex.org/W2790860809","https://openalex.org/W2796027538","https://openalex.org/W2800049629","https://openalex.org/W4211007335","https://openalex.org/W4213068365","https://openalex.org/W4292078529"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4378767041","https://openalex.org/W4210969441","https://openalex.org/W4313271080","https://openalex.org/W2050612014","https://openalex.org/W3166167233","https://openalex.org/W2387128994","https://openalex.org/W2765931357","https://openalex.org/W2906568202"],"abstract_inverted_index":{"Interval-valued":[0],"Pythagorean":[1,36,47],"fuzzy":[2,14,37,48],"set":[3,15],"is":[4,74],"one":[5],"of":[6,10,33,69],"the":[7,11,18,21,31,70,83,119],"successful":[8],"extensions":[9],"interval-valued":[12,35,46],"intuitionistic":[13],"for":[16,106],"handling":[17],"uncertainties":[19],"in":[20,26,99,124],"data.":[22],"Under":[23],"this":[24,27],"environment,":[25],"paper":[28],"we":[29],"introduce":[30],"notion":[32],"induced":[34,45,71],"Einstein":[38,49],"ordered":[39],"weighted":[40],"geometric":[41,51],"(I-IVPFEOWG)":[42],"operator":[43,53],"and":[44,118],"hybrid":[50],"(I-IVPFEHG)":[52],"along":[54],"with":[55],"their":[56],"some":[57],"basic":[58],"properties":[59],"such":[60],"as,":[61],"idempotency,":[62],"boundedness,":[63],"commutatively,":[64],"monotonicity.":[65],"The":[66],"main":[67],"advantage":[68],"aggregation":[72],"operators":[73,77,115],"that,":[75],"these":[76,93,114],"are":[78],"more":[79],"suitable":[80],"to":[81],"aggregate":[82],"individual":[84],"preference":[85,90],"relations":[86],"into":[87],"a":[88,96,104],"collective":[89],"relation.":[91],"Therefore":[92],"methods":[94],"play":[95],"vigorous":[97],"role":[98],"daily":[100],"life":[101],"problems.":[102],"Furthermore,":[103],"method":[105],"multi-attribute":[107],"group":[108],"decision-making":[109],"(MAGDM)":[110],"problems":[111],"based":[112],"on":[113],"was":[116],"developed,":[117],"operational":[120],"procedures":[121],"were":[122],"explained":[123],"detail.":[125]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
