{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:06Z","timestamp":1760242506483,"version":"build-2065373602"},"reference-count":8,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,10,16]],"date-time":"2017-10-16T00:00:00Z","timestamp":1508112000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Neutrosophic    N   -structures with applications in     B C K \/ B C I    -algebras is discussed. The notions of a neutrosophic    N   -subalgebra and a (closed) neutrosophic    N   -ideal in a     B C K \/ B C I    -algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic    N   -subalgebra and a neutrosophic    N   -ideal are considered, and relations between a neutrosophic    N   -subalgebra and a neutrosophic    N   -ideal are stated. Conditions for a neutrosophic    N   -ideal to be a closed neutrosophic    N   -ideal are provided.<\/jats:p>","DOI":"10.3390\/info8040128","type":"journal-article","created":{"date-parts":[[2017,10,16]],"date-time":"2017-10-16T11:11:09Z","timestamp":1508152269000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Neutrosophic N-Structures Applied to BCK\/BCI-Algebras"],"prefix":"10.3390","volume":"8","author":[{"given":"Young","family":"Jun","sequence":"first","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Mathematics & Science Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3871-217X","authenticated-orcid":false,"given":"Hashem","family":"Bordbar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shiraz University, Shiraz 7616914111, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,16]]},"reference":[{"key":"ref_1","first-page":"19","article-title":"On axiom systems of propositional calculi","volume":"42","author":"Imai","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_2","first-page":"26","article-title":"An algebra related with a propositional calculus","volume":"42","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_3","first-page":"417","article-title":"\ud835\udca9-ideals of BCK\/BCI-algebras","volume":"22","author":"Jun","year":"2009","journal-title":"J. Chungcheong Math. Soc."},{"key":"ref_4","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. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_6","unstructured":"Huang, Y.S. (2006). BCI-Algebra, Science Press."},{"key":"ref_7","unstructured":"Meng, J., and Jun, Y.B. (1994). BCK-Algebras, Kyungmoon Sa Co."},{"key":"ref_8","unstructured":"Khan, M., Amis, S., Smarandache, F., and Jun, Y.B. (2017). Neutrosophic \ud835\udca9-structures and their applications in semigroups. Ann. Fuzzy Math. Inform., submitted."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/4\/128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:47:25Z","timestamp":1760208445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/8\/4\/128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,16]]},"references-count":8,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["info8040128"],"URL":"https:\/\/doi.org\/10.3390\/info8040128","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2017,10,16]]}}}