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On Some Generalized Structures in Fuzzy Soft Topological Spaces |
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PP: 107-115 |
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Author(s) |
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Sabir Hussain,
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Abstract |
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| 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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