{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T11:38:41Z","timestamp":1762429121241,"version":"3.41.2"},"reference-count":24,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>In 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non\u2010standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The paper investigates the possible relations between INSs and topology.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Relations on INSs and neutrosophic topology.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>Clearly, the paper is confined to IFSs and NSs.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The main applications are in the mathematical field.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper shows original results on fuzzy sets and topology.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944849","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:00:38Z","timestamp":1243666838000},"page":"621-624","source":"Crossref","is-referenced-by-count":42,"title":["Interval neutrosophic sets and topology"],"prefix":"10.1108","volume":"38","author":[{"given":"Francisco","family":"Gallego Lupi\u00e1\u00f1ez","sequence":"first","affiliation":[]}],"member":"140","reference":[{"key":"key2022021419511732400_b1","unstructured":"Atanassov, K.T. (1983), \u201cIntuitionistic fuzzy sets\u201d, paper presented at the VII ITKR's Session, Sofia, June."},{"key":"key2022021419511732400_b2","doi-asserted-by":"crossref","unstructured":"Atanassov, K.T. (1986), \u201cIntuitionistic fuzzy sets\u201d, Fuzzy Sets and Systems, Vol. 20, pp. 87\u201096.","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"key2022021419511732400_b3","doi-asserted-by":"crossref","unstructured":"Atanassov, K.T. (1988), \u201cReview and new results on intuitionistic fuzzy sets\u201d, preprint IM\u2010MFAIS\u20101\u201088, Sofia.","DOI":"10.1016\/0165-0114(89)90215-7"},{"key":"key2022021419511732400_b4","unstructured":"Bayhan, S. and \u00c7oker, D. (2003), \u201cOn T1 and T2 separation axioms in intuitionistic fuzzy topological spaces\u201d, J. Fuzzy Math., Vol. 11, pp. 581\u201092."},{"key":"key2022021419511732400_b5","unstructured":"\u00c7oker, D. (1996), \u201cAn introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces\u201d, J. Fuzzy Math, Vol. 4, pp. 749\u201064."},{"key":"key2022021419511732400_b6","doi-asserted-by":"crossref","unstructured":"\u00c7oker, D. (1997), \u201cAn introduction to intuitionistic fuzzy topologial spaces\u201d, Fuzzy Sets and Systems, Vol. 88, pp. 81\u20109.","DOI":"10.1016\/S0165-0114(96)00076-0"},{"key":"key2022021419511732400_b7","unstructured":"\u00c7oker, D. and E\u015f, A.H. (1995), \u201cOn fuzzy compactness in intuitionistic fuzzy topological spaces\u201d, J. Fuzzy Math., Vol. 3, pp. 899\u2010909."},{"key":"key2022021419511732400_b8","unstructured":"E\u015f, A.H. and \u00c7oker, D. (1996), \u201cMore on fuzzy compactness in intuitionistic fuzzy topological spaces\u201d, Notes IFS, Vol. 2 No. 1, pp. 4\u201010."},{"key":"key2022021419511732400_b9","unstructured":"G\u00fcr\u00e7ay, H., \u00c7oker, D. and E\u015f, A.H. (1997), \u201cOn fuzzy continuity in intuitionistic fuzzy topological spaces\u201d, J. Fuzzy Math., Vol. 5, pp. 365\u201078."},{"key":"key2022021419511732400_b10","doi-asserted-by":"crossref","unstructured":"Hanafy, J.H. (2003), \u201cCompletely continuous functions in intuitionistic fuzzy topological spaces\u201d, Czech. Math. J., Vol. 53 No. 128, pp. 793\u2010803.","DOI":"10.1023\/B:CMAJ.0000024523.64828.31"},{"key":"key2022021419511732400_b11","unstructured":"Hur, K., Kim, J.H. and Ryou, J.H. (2004), \u201cIntuitionistic fuzzy topologial spaces\u201d, J. Korea Soc. Math. Educ., Ser B, Vol. 11, pp. 243\u201065."},{"key":"key2022021419511732400_b12","unstructured":"Lee, S.J. and Lee, E.P. (2000), \u201cThe category of intuitionistic fuzzy topological spaces\u201d, Bull. Korean Math. Soc., Vol. 37, pp. 63\u201076."},{"key":"key2022021419511732400_b13","unstructured":"Lupi\u00e1\u00f1ez, F.G. (2004a), \u201cHausdorffness in intuitionistic fuzzy topological spaces\u201d, J. 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(2007), \u201cCovering properties in intuitionistic fuzzy topological spaces\u201d, Kybernetes, Vol. 36, pp. 749\u201053.","DOI":"10.1108\/03684920710749811"},{"key":"key2022021419511732400_b18","doi-asserted-by":"crossref","unstructured":"Lupi\u00e1\u00f1ez, F.G. (2008), \u201cOn neutrosophic topology\u201d, Kybernetes, Vol. 37 No. 6, pp. 797\u2010800.","DOI":"10.1108\/03684920810876990"},{"key":"key2022021419511732400_b19","unstructured":"Robinson, A. (1996), Non\u2010standard Analysis, Princeton University Press, Princeton, NJ."},{"key":"key2022021419511732400_b20","unstructured":"Smarandache, F. (2002), \u201cA unifying field in logics: neutrosophic logic\u201d, Multiple\u2010valued Logic, Vol. 8, pp. 385\u2010438."},{"key":"key2022021419511732400_b21","unstructured":"Smarandache, F. (2003), \u201cDefinition of neutrosophic logic. A generalization of the intuitionistic fuzzy logic\u201d, Proc. 3rd Conf. Eur. Soc. Fuzzy Logic Tech. 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