{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T19:00:55Z","timestamp":1768071655406,"version":"3.49.0"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,4,9]],"date-time":"2018-04-09T00:00:00Z","timestamp":1523232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>For     i , j , k , l , m , n \u2208 { 1 , 2 , 3 , 4 }    , the notion of     ( T ( i , j ) , I ( k , l ) , F ( m , n ) )    -interval neutrosophic subalgebra in     B C K \/ B C I    -algebra is introduced, and their properties and relations are investigated. The notion of interval neutrosophic length of an interval neutrosophic set is also introduced, and related properties are investigated.<\/jats:p>","DOI":"10.3390\/axioms7020023","type":"journal-article","created":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T13:06:08Z","timestamp":1523365568000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Interval Neutrosophic Sets with Applications in BCK\/BCI-Algebra"],"prefix":"10.3390","volume":"7","author":[{"given":"Young","family":"Jun","sequence":"first","affiliation":[{"name":"Department of Mathematics Education Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seon","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju 52828, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Mathematics &amp; Science Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,9]]},"reference":[{"key":"ref_1","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_2","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_3","unstructured":"Wang, H., Smarandache, F., Zhang, Y.Q., and Sunderraman, R. (2005). Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis."},{"key":"ref_4","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Reserch Press."},{"key":"ref_5","first-page":"287","article-title":"Neutrosophic set-a generalization of the intuitionistic fuzzy set","volume":"24","author":"Smarandache","year":"2005","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, H., Zhang, Y., and Sunderraman, R. (2005, January 25\u201327). Truth-value based interval neutrosophic sets. Proceedings of the 2005 IEEE International Conference on Granular Computing, Beijing, China.","DOI":"10.1109\/GRC.2005.1547284"},{"key":"ref_7","first-page":"19","article-title":"On axiom systems of propositional calculi","volume":"42","author":"Imai","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_8","first-page":"26","article-title":"An algebra related with a propositional calculus","volume":"42","year":"1966","journal-title":"Proc. Jpn. Acad."},{"key":"ref_9","unstructured":"Huang, Y.S. (2006). BCI-Algebra, Science Press."},{"key":"ref_10","unstructured":"Meng, J., and Jun, Y.B. (1994). BCK-Algebra, Kyungmoon Sa Co."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.30948\/afmi.2018.15.1.17","article-title":"Hyperfuzzy subalgebra of BCK\/BCI-algebra","volume":"15","author":"Jun","year":"2018","journal-title":"Ann. Fuzzy Math. Inf."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/2\/23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:01Z","timestamp":1760194801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/2\/23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,9]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["axioms7020023"],"URL":"https:\/\/doi.org\/10.3390\/axioms7020023","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,9]]}}}