{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T21:50:04Z","timestamp":1775771404005,"version":"3.50.1"},"reference-count":9,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T00:00:00Z","timestamp":1745625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2025R231"],"award-info":[{"award-number":["PNURSP2025R231"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures within this algebraic context. We demonstrate a bidirectional relationship between SBCK-subalgebras and their level sets, proving that each level set derived from a bipolar fuzzy SBCK-subalgebra constitutes a subalgebra, and, conversely, each such subalgebra defines an associated level set. This duality emphasizes the structural interplay between bipolar fuzzy logic and the Sheffer stroke operation in BCK-algebras.<\/jats:p>","DOI":"10.3390\/axioms14050331","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bipolar Fuzzy Sheffer Stroke in BCK-Algebras"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6514-4027","authenticated-orcid":false,"given":"Tahsin","family":"Oner","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, 35100 \u0130zmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0921-6054","authenticated-orcid":false,"given":"Rajesh","family":"Neelamegarajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-7914","authenticated-orcid":false,"given":"Ravi Kumar","family":"Bandaru","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal S.","family":"Alali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.3792\/pja\/1195522169","article-title":"On axiom systems of proposional calculi, XIV","volume":"42","author":"Imai","year":"1966","journal-title":"Proc. Jpn. Acad. Ser. A, Math. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1090\/S0002-9947-1913-1500960-1","article-title":"A set of five independent postulates for Boolean algebras, with application to logical constants","volume":"14","author":"Sheffer","year":"1913","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1020542009983","article-title":"Short single axioms for Boolean algebra","volume":"29","author":"McCune","year":"2002","journal-title":"J. Autom. Reason."},{"key":"ref_4","first-page":"19","article-title":"Sheffer operation in ortholattices","volume":"44","author":"Chajda","year":"2005","journal-title":"Acta Univ. Palack. Olomuc. Fac.Rerum Natur. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1515\/math-2017-0075","article-title":"The Sheffer stroke operation reducts of basic algebras","volume":"15","author":"Oner","year":"2017","journal-title":"Open Math."},{"key":"ref_6","first-page":"245","article-title":"Relation between Sheffer stroke operation and Hilbert algebras","volume":"14","author":"Oner","year":"2021","journal-title":"Categ. Gen. Algebr. Struct. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"381","DOI":"10.7151\/dmgaa.1368","article-title":"On Sheffer stroke UP-algebras","volume":"41","author":"Oner","year":"2021","journal-title":"Discuss. Math. Algebra Appl."},{"key":"ref_8","first-page":"247","article-title":"Class of Sheffer Stroke BCK-Algebras, Analele Stiintice ale Universitatii Ovidius Constanta","volume":"30","author":"Oner","year":"2022","journal-title":"Ser. Mat."},{"key":"ref_9","unstructured":"Zhang, W.R. (1998, January 4\u20139). Bipolar fuzzy sets. Proceedings of the FUZZ-IEEE, Anchorage, AK, USA."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/331\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:22:00Z","timestamp":1760030520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/331"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,26]]},"references-count":9,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050331"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050331","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,26]]}}}