{"id":"https://openalex.org/W2911336948","doi":"https://doi.org/10.3390/sym11020180","title":"Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators","display_name":"Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators","publication_year":2019,"publication_date":"2019-02-02","ids":{"openalex":"https://openalex.org/W2911336948","doi":"https://doi.org/10.3390/sym11020180","mag":"2911336948"},"language":"en","primary_location":{"id":"doi:10.3390/sym11020180","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020180","pdf_url":"https://www.mdpi.com/2073-8994/11/2/180/pdf?version=1549173338","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/2073-8994/11/2/180/pdf?version=1549173338","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101840630","display_name":"Aliya Fahmi","orcid":"https://orcid.org/0000-0003-1049-430X"},"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":"Aliya Fahmi","raw_affiliation_strings":["Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020344801","display_name":"Fazli Amin","orcid":"https://orcid.org/0000-0001-7211-9324"},"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":false,"raw_author_name":"Fazli Amin","raw_affiliation_strings":["Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of mathematics, Hazara University Mansehra, Dhodial 21130, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026770895","display_name":"Madad Khan","orcid":"https://orcid.org/0000-0003-0044-961X"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Madad Khan","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus 22060, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012703845","display_name":"Florent\u00edn Smarandache","orcid":"https://orcid.org/0000-0002-5560-5926"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Florentin Smarandache","raw_affiliation_strings":["Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101840630"],"corresponding_institution_ids":["https://openalex.org/I263208278"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.9612,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.936121,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"11","issue":"2","first_page":"180","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994999766349792,"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":0.9994999766349792,"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":0.980400025844574,"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":0.955299973487854,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.676794707775116},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.6514399647712708},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5735368132591248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.537675142288208},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4337753355503082},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37030744552612305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3601740598678589},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32540416717529297},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2805480360984802},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1759570837020874},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08765709400177002},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05045825242996216}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.676794707775116},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.6514399647712708},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5735368132591248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.537675142288208},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4337753355503082},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37030744552612305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3601740598678589},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32540416717529297},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2805480360984802},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1759570837020874},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08765709400177002},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05045825242996216},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11020180","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020180","pdf_url":"https://www.mdpi.com/2073-8994/11/2/180/pdf?version=1549173338","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:f5f3814716d2484bba14047640ab135c","is_oa":true,"landing_page_url":"https://doaj.org/article/f5f3814716d2484bba14047640ab135c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 11, Iss 2, p 180 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/2/180/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym11020180","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/sym11020180","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020180","pdf_url":"https://www.mdpi.com/2073-8994/11/2/180/pdf?version=1549173338","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":0.8299999833106995,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2911336948.pdf","grobid_xml":"https://content.openalex.org/works/W2911336948.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1991446918","https://openalex.org/W1993810822","https://openalex.org/W1995972849","https://openalex.org/W2018326882","https://openalex.org/W2029982592","https://openalex.org/W2031345712","https://openalex.org/W2041280856","https://openalex.org/W2060599483","https://openalex.org/W2064974864","https://openalex.org/W2067217421","https://openalex.org/W2068402605","https://openalex.org/W2074029308","https://openalex.org/W2084063803","https://openalex.org/W2140034637","https://openalex.org/W2165024836","https://openalex.org/W2762077894","https://openalex.org/W2901266101","https://openalex.org/W4210457345","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3146154164","https://openalex.org/W658450699","https://openalex.org/W2122054506","https://openalex.org/W4388249720","https://openalex.org/W2091620812","https://openalex.org/W642163281","https://openalex.org/W3210394160","https://openalex.org/W2014786470","https://openalex.org/W2077860847"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,78],"new":[4,25],"concept":[5],"of":[6],"the":[7,31,85],"triangular":[8,32,40,50,69],"neutrosophic":[9,33,41,51,70],"cubic":[10,34,42,52,71],"fuzzy":[11,35,43,53,72],"numbers":[12],"(TNCFNs),":[13],"their":[14,63],"score":[15],"and":[16,49,88,93],"accuracy":[17],"functions":[18],"are":[19,60],"introduced.":[20],"Based":[21],"on":[22],"TNCFNs,":[23],"some":[24],"Einstein":[26,36,44,54],"aggregation":[27],"operators,":[28],"such":[29],"as":[30],"weighted":[37,46,56],"averaging":[38,47,57],"(TNCFEWA),":[39],"ordered":[45],"(TNCFEOWA)":[48],"hybrid":[55],"(TNCFEHWA)":[58],"operators":[59],"developed.":[61],"Furthermore,":[62],"application":[64],"to":[65,83,89],"multiple-attribute":[66],"decision-making":[67],"with":[68],"(TNCF)":[73],"information":[74],"is":[75,81],"discussed.":[76],"Finally,":[77],"practical":[79],"example":[80],"given":[82],"verify":[84],"developed":[86],"approach":[87],"demonstrate":[90],"its":[91],"practicality":[92],"effectiveness.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}