{"id":"https://openalex.org/W4386525642","doi":"https://doi.org/10.3390/sym15091717","title":"Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras","display_name":"Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras","publication_year":2023,"publication_date":"2023-09-07","ids":{"openalex":"https://openalex.org/W4386525642","doi":"https://doi.org/10.3390/sym15091717"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091717","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1717/pdf?version=1694086783","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/2073-8994/15/9/1717/pdf?version=1694086783","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001324001","display_name":"Abdullah Assiry","orcid":null},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdullah Assiry","raw_affiliation_strings":["Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 21955, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011037105","display_name":"Amir Baklouti","orcid":"https://orcid.org/0000-0002-6652-5868"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Amir Baklouti","raw_affiliation_strings":["Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 21955, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6652-5868","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, Mecca 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011037105"],"corresponding_institution_ids":["https://openalex.org/I199693650"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1931,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55348155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"9","first_page":"1717","last_page":"1717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9955000281333923,"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":0.9950000047683716,"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/semigroup","display_name":"Semigroup","score":0.5486952066421509},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5089924335479736},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.476910799741745},{"id":"https://openalex.org/keywords/surface-finish","display_name":"Surface finish","score":0.460247665643692},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4539700150489807},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.45304277539253235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4264976978302002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3906855881214142},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36860743165016174},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.36497294902801514},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3026401996612549},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.136540025472641}],"concepts":[{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5486952066421509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5089924335479736},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.476910799741745},{"id":"https://openalex.org/C71039073","wikidata":"https://www.wikidata.org/wiki/Q3439090","display_name":"Surface finish","level":2,"score":0.460247665643692},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4539700150489807},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.45304277539253235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4264976978302002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3906855881214142},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36860743165016174},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.36497294902801514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3026401996612549},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.136540025472641},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15091717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091717","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1717/pdf?version=1694086783","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:d5b396ba141e4793a46ead5b9b778c7c","is_oa":false,"landing_page_url":"https://doaj.org/article/d5b396ba141e4793a46ead5b9b778c7c","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 15, Iss 9, p 1717 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/9/1717/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15091717","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/sym15091717","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091717","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1717/pdf?version=1694086783","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":0.75,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386525642.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1515119244","https://openalex.org/W1971424330","https://openalex.org/W1982907249","https://openalex.org/W1989832241","https://openalex.org/W2102543282","https://openalex.org/W2279764372","https://openalex.org/W2345854887","https://openalex.org/W2549504134","https://openalex.org/W2586356223","https://openalex.org/W2735573330","https://openalex.org/W2809720492","https://openalex.org/W2959960327","https://openalex.org/W2966380844","https://openalex.org/W2982257117","https://openalex.org/W3003181796","https://openalex.org/W3005671167","https://openalex.org/W3005880828","https://openalex.org/W3028181872","https://openalex.org/W3165474212","https://openalex.org/W3185376175","https://openalex.org/W4200015000","https://openalex.org/W4214865273","https://openalex.org/W4289783231","https://openalex.org/W4300818790","https://openalex.org/W4309271266","https://openalex.org/W4310015403","https://openalex.org/W4379143839","https://openalex.org/W4382058126","https://openalex.org/W7061649479"],"related_works":["https://openalex.org/W4386799044","https://openalex.org/W2773208253","https://openalex.org/W2560646951","https://openalex.org/W4297454206","https://openalex.org/W65104662","https://openalex.org/W1871748041","https://openalex.org/W2362286668","https://openalex.org/W2133382151","https://openalex.org/W2153339597","https://openalex.org/W1528412344"],"abstract_inverted_index":{"This":[0],"paper":[1],"explores":[2],"the":[3,19,46,59,74,79,84,91,97,120,131,164],"concept":[4],"of":[5,24,48,61,76,86,93,99,122,133,155,166,204],"Generalized":[6,25,62,70,94,123,180],"Roughness":[7,95,124],"in":[8,13,58,69,96,125,157,172,179],"LA-Semigroups":[9,156],"and":[10,22,40,55,83,102,108,115,128,138,153,169,176,189,195,207],"its":[11,28,113],"applications":[12,121],"various":[14],"mathematical":[15,49,126,148],"disciplines.":[16],"We":[17,89,145],"highlight":[18],"fundamental":[20],"properties":[21,114],"structures":[23],"Roughness,":[26,71],"examining":[27],"relationships":[29],"with":[30],"Fuzzy":[31],"Lie":[32],"Algebras,":[33],"Order":[34],"Theory,":[35],"Lattice":[36],"Structures,":[37,39],"Algebraic":[38],"Categorical":[41],"Perspectives.":[42],"Moreover,":[43],"we":[44,118,161,186],"investigate":[45],"potential":[47],"modeling,":[50],"optimization":[51,132],"techniques,":[52,185],"data":[53,167,193],"analysis,":[54],"machine":[56,170,196],"learning":[57,171,197],"context":[60,98],"Roughness.":[63,181],"Our":[64],"findings":[65],"reveal":[66],"important":[67],"results":[68],"such":[72],"as":[73],"preservation":[75],"roughness":[77,87,134],"under":[78],"fuzzy":[80],"equivalence":[81],"relation":[82],"composition":[85],"sets.":[88],"demonstrate":[90],"significance":[92],"order":[100],"theory":[101],"lattice":[103],"structures,":[104],"presenting":[105],"key":[106],"propositions":[107],"a":[109],"theorem":[110],"that":[111],"elucidate":[112],"relationships.":[116],"Furthermore,":[117],"explore":[119],"modeling":[127],"optimization,":[129],"highlighting":[130],"measures,":[135],"parameter":[136],"estimation,":[137],"decision-making":[139,209],"processes":[140],"related":[141],"to":[142,200],"LA-Semigroup":[143,205],"operations.":[144],"showcase":[146],"how":[147,192],"techniques":[149],"can":[150,198],"enhance":[151],"understanding":[152,203],"utilization":[154],"practical":[158],"scenarios.":[159],"Lastly,":[160],"delve":[162],"into":[163,191],"role":[165],"analysis":[168,194],"uncovering":[173],"patterns,":[174],"relationships,":[175],"predictive":[177],"models":[178],"By":[182],"leveraging":[183],"these":[184],"provide":[187],"examples":[188],"insights":[190],"contribute":[199],"enhancing":[201],"our":[202],"behavior":[206],"supporting":[208],"processes.":[210]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
