{"id":"https://openalex.org/W4294168233","doi":"https://doi.org/10.3390/sym14091812","title":"Some Characterizations of Certain Complex Fuzzy Subgroups","display_name":"Some Characterizations of Certain Complex Fuzzy Subgroups","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4294168233","doi":"https://doi.org/10.3390/sym14091812"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091812","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091812","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1812/pdf?version=1662023297","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/2073-8994/14/9/1812/pdf?version=1662023297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055637763","display_name":"Abeer Ali Alharbi","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abeer Ali Alharbi","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034560922","display_name":"Dilshad Alghazzawi","orcid":"https://orcid.org/0000-0002-8330-2818"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Dilshad Alghazzawi","raw_affiliation_strings":["Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-8330-2818","affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034560922"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6755,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7263141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1812","last_page":"1812"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9909999966621399,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.6253853440284729},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6096619367599487},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5584266781806946},{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.5351418256759644},{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.4846556782722473},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.47972622513771057},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.441873162984848},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4252077639102936},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3874058127403259},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38043028116226196},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3194524049758911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27762216329574585},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25440385937690735},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2474983036518097}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6253853440284729},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6096619367599487},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5584266781806946},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.5351418256759644},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.4846556782722473},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.47972622513771057},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.441873162984848},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4252077639102936},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3874058127403259},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38043028116226196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3194524049758911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27762216329574585},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25440385937690735},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2474983036518097},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14091812","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091812","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1812/pdf?version=1662023297","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:7eea53732bf3408a900b9e93d30636c2","is_oa":true,"landing_page_url":"https://doaj.org/article/7eea53732bf3408a900b9e93d30636c2","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 14, Iss 9, p 1812 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1812/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091812","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; Volume 14; Issue 9; Pages: 1812","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091812","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091812","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1812/pdf?version=1662023297","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4294168233.pdf"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1969882757","https://openalex.org/W1972528888","https://openalex.org/W1976236488","https://openalex.org/W1990527277","https://openalex.org/W1992354936","https://openalex.org/W2014045179","https://openalex.org/W2019332267","https://openalex.org/W2044315800","https://openalex.org/W2068883966","https://openalex.org/W2089622054","https://openalex.org/W2090795068","https://openalex.org/W2094208309","https://openalex.org/W2097403045","https://openalex.org/W2265831291","https://openalex.org/W2305226781","https://openalex.org/W2571042968","https://openalex.org/W2742484806","https://openalex.org/W2793505150","https://openalex.org/W2900416207","https://openalex.org/W2953264884","https://openalex.org/W2977985768","https://openalex.org/W3001588749","https://openalex.org/W3041528574","https://openalex.org/W3081525434","https://openalex.org/W3081653322","https://openalex.org/W3096389194","https://openalex.org/W3106894738","https://openalex.org/W3198259010","https://openalex.org/W3202206548","https://openalex.org/W4205167602","https://openalex.org/W4206318007","https://openalex.org/W4210778630","https://openalex.org/W4210893248","https://openalex.org/W4211007335","https://openalex.org/W4213071690","https://openalex.org/W4224301740","https://openalex.org/W6693704333","https://openalex.org/W6742488187","https://openalex.org/W6749257683","https://openalex.org/W6764460864","https://openalex.org/W6765083652","https://openalex.org/W6780388041","https://openalex.org/W6800648386","https://openalex.org/W6806227516","https://openalex.org/W6807971960","https://openalex.org/W6957941457","https://openalex.org/W6958008685"],"related_works":["https://openalex.org/W3163209247","https://openalex.org/W3101617115","https://openalex.org/W3198699946","https://openalex.org/W4387502800","https://openalex.org/W1486684451","https://openalex.org/W2166637398","https://openalex.org/W2087021805","https://openalex.org/W2374152511","https://openalex.org/W2066929655","https://openalex.org/W4312800262"],"abstract_inverted_index":{"The":[0],"complex":[1],"fuzzy":[2,25,28,31,43,58,64,86,102],"environment":[3],"is":[4],"an":[5,94],"innovative":[6],"tool":[7],"to":[8,56,75],"handle":[9],"ambiguous":[10],"situations":[11],"in":[12],"different":[13],"mathematical":[14],"problems.":[15],"In":[16],"this":[17,73],"article,":[18],"we":[19,46,98],"commence":[20],"the":[21,38,48,52,69,84,100,105],"abstraction":[22],"of":[23,37,51,72,104],"(\u03c1,\u03b7)-complex":[24,27,30,42,57,63,85,101],"sets,":[26],"subgroupoid,":[29],"subgroups":[32],"and":[33,66,92],"describe":[34],"important":[35],"examples":[36],"symmetric":[39],"group":[40,53,76,91],"under":[41],"sets.":[44],"Additionally,":[45],"discuss":[47],"conjugacy":[49],"class":[50],"with":[54],"respect":[55],"normal":[59,87],"subgroups.":[60],"We":[61,79],"define":[62],"cosets":[65],"elaborate":[67],"upon":[68],"certain":[70],"operation":[71],"analog":[74],"theoretic":[77],"operation.":[78],"prove":[80],"that":[81],"factors":[82],"regarding":[83],"subgroup":[88,103],"form":[89],"a":[90],"establish":[93],"ordinary":[95],"homomorphism.":[96],"Moreover,":[97],"create":[99],"factor":[106],"group.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}