{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T11:37:46Z","timestamp":1773056266473,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,1]],"date-time":"2022-09-01T00:00:00Z","timestamp":1661990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Abdulaziz University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (\u03c1,\u03b7)-complex fuzzy sets, (\u03c1,\u03b7)-complex fuzzy subgroupoid, (\u03c1,\u03b7)-complex fuzzy subgroups and describe important examples of the symmetric group under (\u03c1,\u03b7)-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to (\u03c1,\u03b7)-complex fuzzy normal subgroups. We define (\u03c1,\u03b7)-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors regarding the (\u03c1,\u03b7)-complex fuzzy normal subgroup form a group and establish an ordinary homomorphism. Moreover, we create the (\u03c1,\u03b7)-complex fuzzy subgroup of the factor group.<\/jats:p>","DOI":"10.3390\/sym14091812","type":"journal-article","created":{"date-parts":[[2022,9,2]],"date-time":"2022-09-02T00:19:01Z","timestamp":1662077941000},"page":"1812","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Some Characterizations of Certain Complex Fuzzy Subgroups"],"prefix":"10.3390","volume":"14","author":[{"given":"Abeer Ali","family":"Alharbi","sequence":"first","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8330-2818","authenticated-orcid":false,"given":"Dilshad","family":"Alghazzawi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Rabigh 25732, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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