{"id":"https://openalex.org/W4393352823","doi":"https://doi.org/10.3390/sym16040402","title":"An Introduction to Single-Valued Neutrosophic Primal Theory","display_name":"An Introduction to Single-Valued Neutrosophic Primal Theory","publication_year":2024,"publication_date":"2024-03-29","ids":{"openalex":"https://openalex.org/W4393352823","doi":"https://doi.org/10.3390/sym16040402"},"language":"en","primary_location":{"id":"doi:10.3390/sym16040402","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040402","pdf_url":"https://www.mdpi.com/2073-8994/16/4/402/pdf?version=1711729312","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/2073-8994/16/4/402/pdf?version=1711729312","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002885956","display_name":"Fahad Alsharari","orcid":"https://orcid.org/0000-0003-3818-3597"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fahad Alsharari","raw_affiliation_strings":["Department of Mathematics, College of Science, Jouf University, Sakaka 72311, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3818-3597","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University, Sakaka 72311, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092690151","display_name":"Hanan Alohali","orcid":"https://orcid.org/0009-0005-0052-4976"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hanan Alohali","raw_affiliation_strings":["Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0005-0052-4976","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026576309","display_name":"Yaser Saber","orcid":"https://orcid.org/0000-0003-4795-3469"},"institutions":[{"id":"https://openalex.org/I195631090","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60","country_code":"SA","type":"education","lineage":["https://openalex.org/I195631090"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Yaser Saber","raw_affiliation_strings":["Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4795-3469","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]}]},{"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"]},{"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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026576309"],"corresponding_institution_ids":["https://openalex.org/I195631090"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.383,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81357738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"4","first_page":"402","last_page":"402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.989799976348877,"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":0.989799976348877,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9728999733924866,"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":0.9598000049591064,"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/mathematics","display_name":"Mathematics","score":0.6258749961853027},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.53938889503479},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5340415835380554},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3803866505622864},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36445367336273193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34248971939086914},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3070746958255768},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29436373710632324},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22268906235694885},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13675835728645325}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6258749961853027},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.53938889503479},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5340415835380554},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3803866505622864},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36445367336273193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34248971939086914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3070746958255768},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29436373710632324},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22268906235694885},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13675835728645325}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym16040402","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040402","pdf_url":"https://www.mdpi.com/2073-8994/16/4/402/pdf?version=1711729312","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:digitalrepository.unm.edu:math_fsp-1861","is_oa":true,"landing_page_url":"https://digitalrepository.unm.edu/math_fsp/720","pdf_url":null,"source":{"id":"https://openalex.org/S4377196368","display_name":"UNM\u2019s Digital Repository (University of New Mexico)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169521973","host_organization_name":"University of New Mexico","host_organization_lineage":["https://openalex.org/I169521973"],"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":"Branch Mathematics and Statistics Faculty and Staff Publications","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:b6e1589ca2ce4874b6536c087292450d","is_oa":false,"landing_page_url":"https://doaj.org/article/b6e1589ca2ce4874b6536c087292450d","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 4, p 402 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16040402","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040402","pdf_url":"https://www.mdpi.com/2073-8994/16/4/402/pdf?version=1711729312","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":[{"id":"https://metadata.un.org/sdg/10","score":0.5799999833106995,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2716117995","display_name":null,"funder_award_id":"RSPD2024R860","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393352823.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W58991120","https://openalex.org/W330690783","https://openalex.org/W1595461165","https://openalex.org/W1896774390","https://openalex.org/W2061879449","https://openalex.org/W2085412082","https://openalex.org/W2093545994","https://openalex.org/W2153696615","https://openalex.org/W2273877200","https://openalex.org/W2277376132","https://openalex.org/W2288560581","https://openalex.org/W2324598622","https://openalex.org/W2336484677","https://openalex.org/W2552001947","https://openalex.org/W2588033807","https://openalex.org/W2612715417","https://openalex.org/W2622634640","https://openalex.org/W2891987911","https://openalex.org/W2913663554","https://openalex.org/W3001377282","https://openalex.org/W3009865243","https://openalex.org/W3083448375","https://openalex.org/W4236526037","https://openalex.org/W4242361954","https://openalex.org/W4247655907","https://openalex.org/W4386505603","https://openalex.org/W4386506896","https://openalex.org/W4386519491","https://openalex.org/W4389212472","https://openalex.org/W4392884076","https://openalex.org/W6602379895","https://openalex.org/W6633286288","https://openalex.org/W6635412688","https://openalex.org/W6694498212","https://openalex.org/W6733276414","https://openalex.org/W6734809981"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4309710663","https://openalex.org/W2116865742","https://openalex.org/W2081579710","https://openalex.org/W2371641196","https://openalex.org/W2000850197","https://openalex.org/W2367065563","https://openalex.org/W2980021896","https://openalex.org/W4226227616","https://openalex.org/W3138671984"],"abstract_inverted_index":{"This":[0],"article":[1],"explores":[2],"the":[3,6,25,36,46,75,83,88,96,108],"interconnections":[4],"among":[5],"single-valued":[7,10,29,50,57,70,76,84,91,97,101],"neutrosophic":[8,11,30,51,58,71,77,85,92,98,102],"grill,":[9],"primal":[12,38,42,78,99],"and":[13,20,39,100],"their":[14,17],"stratification,":[15],"uncovering":[16],"fundamental":[18],"characteristics":[19],"correlated":[21],"findings.":[22],"By":[23],"introducing":[24],"notion":[26],"of":[27,48,90,110],"a":[28,32,49,56,69],"primal,":[31,72],"broader":[33],"framework":[34],"including":[35],"fuzzy":[37,41],"intuitionistic":[40],"is":[43,61,80,104],"established.":[44],"Additionally,":[45],"concept":[47,89],"open":[52,93],"local":[53],"function":[54],"for":[55],"topological":[59],"space":[60],"presented.":[62],"We":[63],"introduce":[64],"an":[65],"operator":[66],"based":[67],"on":[68],"illustrating":[73],"that":[74],"topology":[79],"finer":[81],"than":[82],"topology.":[86],"Lastly,":[87],"compatibility":[94],"between":[95],"topologies":[103],"introduced,":[105],"along":[106],"with":[107],"establishment":[109],"several":[111],"equivalent":[112],"conditions":[113],"related":[114],"to":[115],"this":[116],"notion.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}