{"id":"https://openalex.org/W2885123273","doi":"https://doi.org/10.3390/sym10080345","title":"Neutrosophic Duplets of {Zpn,\u00d7} and {Zpq,\u00d7} and Their Properties","display_name":"Neutrosophic Duplets of {Zpn,\u00d7} and {Zpq,\u00d7} and Their Properties","publication_year":2018,"publication_date":"2018-08-17","ids":{"openalex":"https://openalex.org/W2885123273","doi":"https://doi.org/10.3390/sym10080345","mag":"2885123273"},"language":"en","primary_location":{"id":"doi:10.3390/sym10080345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080345","pdf_url":"https://www.mdpi.com/2073-8994/10/8/345/pdf?version=1534500369","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/2073-8994/10/8/345/pdf?version=1534500369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078525741","display_name":"W. B. Vasantha Kandasamy","orcid":"https://orcid.org/0000-0001-9832-1475"},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vasantha Kandasamy W.B.","raw_affiliation_strings":["School of Computer Science and Engineering, VIT, Vellore 632014, India"],"raw_orcid":"https://orcid.org/0000-0001-9832-1475","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, VIT, Vellore 632014, India","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071658857","display_name":"Ilanthenral Kandasamy","orcid":"https://orcid.org/0000-0003-4826-9466"},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ilanthenral Kandasamy","raw_affiliation_strings":["School of Computer Science and Engineering, VIT, Vellore 632014, India"],"raw_orcid":"https://orcid.org/0000-0003-4826-9466","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, VIT, Vellore 632014, India","institution_ids":["https://openalex.org/I876193797"]}]},{"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":["Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA"],"raw_orcid":"https://orcid.org/0000-0002-5560-5926","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071658857"],"corresponding_institution_ids":["https://openalex.org/I876193797"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.0132,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94620168,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"8","first_page":"345","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14500","display_name":"Advanced Mathematical Theories","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14500","display_name":"Advanced Mathematical Theories","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9921000003814697,"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":0.984499990940094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4954797029495239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4911350905895233},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3219049274921417},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2872645854949951}],"concepts":[{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4954797029495239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4911350905895233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3219049274921417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2872645854949951},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10080345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080345","pdf_url":"https://www.mdpi.com/2073-8994/10/8/345/pdf?version=1534500369","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:3ef1dae1dc5747c7b7044cd577765836","is_oa":true,"landing_page_url":"https://doaj.org/article/3ef1dae1dc5747c7b7044cd577765836","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 10, Iss 8, p 345 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/8/345/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym10080345","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/sym10080345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10080345","pdf_url":"https://www.mdpi.com/2073-8994/10/8/345/pdf?version=1534500369","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2885123273.pdf","grobid_xml":"https://content.openalex.org/works/W2885123273.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W58991120","https://openalex.org/W1980564456","https://openalex.org/W2054416947","https://openalex.org/W2140034637","https://openalex.org/W2517034171","https://openalex.org/W2558889492","https://openalex.org/W2579859930","https://openalex.org/W2751840245","https://openalex.org/W2758568055","https://openalex.org/W2768651475","https://openalex.org/W2771003089","https://openalex.org/W2773933146","https://openalex.org/W2800467860","https://openalex.org/W2807665801","https://openalex.org/W2884044414","https://openalex.org/W2952439186","https://openalex.org/W2964162438","https://openalex.org/W2971445734","https://openalex.org/W4211007335","https://openalex.org/W6602379895","https://openalex.org/W6633286288","https://openalex.org/W6719122351","https://openalex.org/W6729990301","https://openalex.org/W6746413040"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W3107994849","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298"],"abstract_inverted_index":{"The":[0],"notions":[1],"of":[2,23,45,57,65],"neutrosophy,":[3],"neutrosophic":[4,7,10,21,58,75,99],"algebraic":[5],"structures,":[6],"duplet":[8],"and":[9,31,49],"triplet":[11],"were":[12],"introduced":[13],"by":[14],"Florentin":[15],"Smarandache.":[16],"In":[17,42,62],"this":[18],"paper,":[19],"the":[20,43,54,63,74],"duplets":[22,59,76,100],"Z":[24,28,32,46,50,66],"p":[25,29,33,35,38,47,51,67,70,79],"n":[26,39,48,71,92],",":[27,53,72,87,89,91],"q":[30,52],"1":[34,68,86],"2":[36,88],"\u2026":[37,69,90],"are":[40,60,82,101],"studied.":[41],"case":[44,64],"complete":[55],"characterization":[56],"given.":[61],"only":[73],"associated":[77],"with":[78],"i":[80,84],"s":[81],"provided;":[83],"=":[85],".":[93],"Some":[94],"open":[95],"problems":[96],"related":[97],"to":[98],"proposed.":[102]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":9}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}