{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:55:11Z","timestamp":1760230511686,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T00:00:00Z","timestamp":1659052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2022R87"],"award-info":[{"award-number":["PNURSP2022R87"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we acquaint new kinds of ideals of BCK-algebras built on tripolar picture fuzzy structures. In fact, the notions of tripolar picture fuzzy ideal, tripolar picture fuzzy implicative ideal (commutative ideal) of BCK-algebra are introduced, and related properties are studied. Also, a relation among tripolar picture fuzzy ideal, and tripolar picture fuzzy implicative ideal is well-known. Furthermore, it is shown that a tripolar picture fuzzy implicative ideal of BCK-algebra may be a tripolar picture fuzzy ideal, but the converse is not correct in common. Further, it is obtained that in an implicative BCK-algebra, the converse of aforementioned statement is true. Finally, the opinion of tripolar picture fuzzy commutative ideal is given, and some useful properties are explored. Many examples are constructed to sport our study.<\/jats:p>","DOI":"10.3390\/sym14081562","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T01:41:16Z","timestamp":1659058876000},"page":"1562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Tripolar Picture Fuzzy Ideals of BCK-Algebras"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5529-0565","authenticated-orcid":false,"given":"Nabilah","family":"Abughazalah","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afaf","family":"Aljuhani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1143-2090","authenticated-orcid":false,"given":"Manivannan","family":"Balamurugan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Vidya Mandir Arts and Science College (Autonomous), Uthangarai 636902, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,29]]},"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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