{"id":"https://openalex.org/W2771003089","doi":"https://doi.org/10.3390/sym9110275","title":"Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups","display_name":"Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups","publication_year":2017,"publication_date":"2017-11-14","ids":{"openalex":"https://openalex.org/W2771003089","doi":"https://doi.org/10.3390/sym9110275","mag":"2771003089"},"language":"en","primary_location":{"id":"doi:10.3390/sym9110275","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9110275","pdf_url":"https://www.mdpi.com/2073-8994/9/11/275/pdf","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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/9/11/275/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100330121","display_name":"Xiaohong Zhang","orcid":"https://orcid.org/0000-0003-2320-0884"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]},{"id":"https://openalex.org/I96733725","display_name":"Shanghai Maritime University","ror":"https://ror.org/04z7qrj66","country_code":"CN","type":"education","lineage":["https://openalex.org/I96733725"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohong Zhang","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science &amp;Technology, Xi\u2019an 710021, China","Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science &amp;Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China","institution_ids":["https://openalex.org/I96733725"]}]},{"author_position":"middle","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"]},{"id":"https://openalex.org/I4210118010","display_name":"Gallup Indian Medical Center","ror":"https://ror.org/02jbzrw51","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1299022934","https://openalex.org/I157850169","https://openalex.org/I4210118010"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Florentin Smarandache","raw_affiliation_strings":["Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA"],"raw_orcid":"https://orcid.org/0000-0002-5560-5926","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA","institution_ids":["https://openalex.org/I4210118010","https://openalex.org/I169521973"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078042468","display_name":"Xingliang Liang","orcid":"https://orcid.org/0000-0002-4517-8684"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingliang Liang","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science &amp;Technology, Xi\u2019an 710021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science &amp;Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100330121"],"corresponding_institution_ids":["https://openalex.org/I51622183","https://openalex.org/I96733725"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":11.8289,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.98658676,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"9","issue":"11","first_page":"275","last_page":"275"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9980000257492065,"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":0.9980000257492065,"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":0.994700014591217,"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":0.9904999732971191,"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/group","display_name":"Group (periodic table)","score":0.6226617097854614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5282639265060425},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4166538715362549},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33594587445259094},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08216768503189087}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6226617097854614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5282639265060425},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4166538715362549},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33594587445259094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08216768503189087},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym9110275","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9110275","pdf_url":"https://www.mdpi.com/2073-8994/9/11/275/pdf","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:b0d6cde24488426cb337e7bd06559e46","is_oa":true,"landing_page_url":"https://doaj.org/article/b0d6cde24488426cb337e7bd06559e46","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 9, Iss 11, p 275 (2017)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/7048307","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Neutrosophic_Duplet_Semi-Group_and_Cancellable_Neutrosophic_Triplet_Groups/7048307","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/2073-8994/9/11/275/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym9110275","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"},{"id":"doi:10.6084/m9.figshare.7048307.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.7048307.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/sym9110275","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9110275","pdf_url":"https://www.mdpi.com/2073-8994/9/11/275/pdf","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":[],"awards":[{"id":"https://openalex.org/G6040557878","display_name":null,"funder_award_id":"61573240","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7365172496","display_name":null,"funder_award_id":"61473239","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2771003089.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1510126807","https://openalex.org/W2011765234","https://openalex.org/W2153696615","https://openalex.org/W2355999078","https://openalex.org/W2517034171","https://openalex.org/W2528304497","https://openalex.org/W2607638685","https://openalex.org/W2617654580","https://openalex.org/W2626173526","https://openalex.org/W2739306068","https://openalex.org/W2755766352","https://openalex.org/W2765449945","https://openalex.org/W2786805307","https://openalex.org/W2964136605","https://openalex.org/W2971445734","https://openalex.org/W6637135071","https://openalex.org/W6728231498","https://openalex.org/W6738466040","https://openalex.org/W6739672959","https://openalex.org/W6745298762","https://openalex.org/W6977626995","https://openalex.org/W7008111447"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"The":[0],"notions":[1],"of":[2,54,78,111,136],"the":[3,15,19,29,61,75,99,109,120,128,134,145],"neutrosophic":[4,7,20,23,39,42,47,55,71,80,83,88,114,122,138,146,150],"triplet":[5,48,123,139],"and":[6,22,45,60,86,108,127,141,148],"duplet":[8,40,43,56,72,84,89,115],"were":[9],"introduced":[10],"by":[11,97],"Florentin":[12],"Smarandache.":[13],"From":[14],"existing":[16],"research":[17],"results,":[18],"triplets":[21,147],"duplets":[24,151],"are":[25,58,91,95,117,125,154],"completely":[26],"different":[27],"from":[28],"classical":[30],"algebra":[31],"structures.":[32],"In":[33],"this":[34],"paper,":[35],"we":[36],"further":[37],"study":[38],"sets,":[41],"semi-groups,":[44],"cancellable":[46,112,121,137],"groups.":[49],"First,":[50],"some":[51,93],"new":[52,76],"properties":[53],"semi-groups":[57,116],"funded,":[59],"following":[62,129],"important":[63,130],"result":[64,131],"is":[65,68,132],"proven:":[66,133],"there":[67],"no":[69],"finite":[70],"semi-group.":[73],"Second,":[74],"concepts":[77],"weak":[79,82,87,113,149],"duplet,":[81],"set,":[85],"semi-group":[90],"introduced,":[92],"examples":[94],"given":[96],"using":[98],"mathematical":[100],"software":[101],"MATLAB":[102],"(MathWorks,":[103],"Inc.,":[104],"Natick,":[105],"MA,":[106],"USA),":[107],"characterizations":[110],"established.":[118],"Third,":[119],"groups":[124],"investigated,":[126],"concept":[135],"group":[140,142],"coincide.":[143],"Finally,":[144],"in":[152],"BCI-algebras":[153],"discussed.":[155]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":30}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
