{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T06:09:27Z","timestamp":1770876567534,"version":"3.50.1"},"reference-count":10,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T00:00:00Z","timestamp":1769299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This research is funded by Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia under Researchers Supporting Project Number","award":["PNURSP2025R231"],"award-info":[{"award-number":["PNURSP2025R231"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study investigates linear Diophantine fuzzy structures within the framework of Sheffer stroke BCK-algebras (SBCK-algebras). We introduce and characterize linear Diophantine fuzzy SBCK-subalgebras and linear Diophantine fuzzy SBCK-ideals, establishing fundamental connections between these fuzzy structures and their corresponding crisp subalgebras and ideals. In particular, we prove that the level sets of linear Diophantine fuzzy SBCK-subalgebras form SBCK-subalgebras, and, conversely, every SBCK-subalgebra gives rise to such a fuzzy structure. Additionally, we show that every linear Diophantine fuzzy SBCK-ideal induces a linear Diophantine fuzzy SBCK-subalgebra; however, the converse does not necessarily hold. Several structural properties, homomorphic images, and intersections of such fuzzy ideals are also examined. These results demonstrate how linear Diophantine logic naturally integrates with Sheffer stroke BCK-algebras and enriches their algebraic behavior.<\/jats:p>","DOI":"10.3390\/axioms15020086","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:05:27Z","timestamp":1769504727000},"page":"86","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sheffer Stroke BCK-Algebras via Linear Diophantine Fuzzy Structures"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal S.","family":"Alali","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6514-4027","authenticated-orcid":false,"given":"Tahsin","family":"Oner","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, Izmir 35100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-7914","authenticated-orcid":false,"given":"Ravikumar","family":"Bandaru","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, VIT-AP University, Andhra Pradesh 522237, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0921-6054","authenticated-orcid":false,"given":"Neelamegarajan","family":"Rajesh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rajah Serfoji Government College, Thanjavur 613005, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"additional","affiliation":[{"name":"Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,25]]},"reference":[{"key":"ref_1","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. Amer. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"247","DOI":"10.2478\/auom-2022-0014","article-title":"Class of Sheffer stroke BCK-algebras","volume":"30","author":"Oner","year":"2022","journal-title":"Analele \u015etiin\u0163ifice ale Universit\u0103\u0163ii Ovidius Constan\u0163a Seria Matematic\u0103"},{"key":"ref_3","first-page":"5417","article-title":"Linear Diophantine fuzzy set and its applications towards multi-attribute decision making problems","volume":"37","author":"Riaz","year":"2019","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"10353","DOI":"10.1007\/s12652-020-02826-x","article-title":"Linear Diophantine fuzzy algebraic structures","volume":"12","year":"2021","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Muhiuddin, G., Al-Tahan, M., Mahboob, A., Ho\u0161kov\u00e1-Mayerov\u00e1, \u0160., and Al-Kaseasbeh, S. (2022). 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