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Information Sciences Letters

Information Sciences Letters

Abstract

Molodstov introduced soft sets to deal with uncertainties and not clear objects. Researchers developed the relationship between soft sets and information systems. Fuzzification of the notions of soft sets and soft topology have been discussed in the literature. In this paper, we define and establish the topological structures of fuzzy soft semi-open sets and fuzzy soft semi-closed sets. We introduce and explore fuzzy soft semi-interior, fuzzy soft semi-closure and fuzzy soft semi-exterior. The relationship between fuzzy soft semi-open(closed), fuzzy soft semi-interior(closure) and fuzzy soft open(closed)sets, fuzzy soft interior(closure) introduced by Chang [C. L. Chang, Journal of Mathematical Analysis and Applications, 24(1), 182- 190(1968)], Tanay and Kandemir [ B. Tanay and M. B. Kandemir, Computers and Mathematics with Applications, 61(10), 2952- 2957(2011)] and further studied by Varol and Aygun [B. P. Varol and H. Aygun, Hacettepe Journal of Mathematics and Statistics, 41(3), 407-419 (2012)] have been discussed. We also initiate and discuss the characterizations and properties of fuzzy soft semi-boundary and establish the behavior of fuzzy soft semiboundary with fuzzy soft semi-interior, fuzzy soft semi-exterior, and fuzzy soft semi-closure. Moreover, we define and explore the characterizations and properties of fuzzy soft semi-continuous and fuzzy soft semi-open mappings in fuzzy soft topological spaces. Theses findings are not only important but also will provide the base for further study on fuzzy soft topology towards practical life applications.

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