Lower Separation Axioms in C ̌ech Fuzzy Soft Closure Spaces

Year 2019, , 1254 - 1269, 01.12.2019

Rasha Majeed , Lina Maıbed

https://doi.org/10.35378/gujs.433174

Cited By: 2

Abstract

By
considering ech fuzzy soft closure spaces , we provide
a basic structure of a fuzzy soft topological space  associated with ech fuzzy
soft closure space  . Separation
axioms, namely,T_İ ( i = 1,2,3 ), semi-
(respectively, pseudo and Uryshon) T2  are studied in both ech fuzzy
soft closure spaces and its associative fuzzy soft topological spaces. It is
shown that hereditary property is satisfied for T_İ  i = 0,1  ,  with respect to ech fuzzy
soft closure space but for other mentioned types of separations axioms,
hereditary property satisfies for closed subspaces of ech fuzzy
soft closure space. Several examples are given to illustrate each type of the
separation axioms and to study the relationship between them.

Keywords

Fuzzy soft set, Fuzzy soft point, C ̌ech fuzzy soft closure operator, Distinct fuzzy soft points, T_i-C ̆ech closure spaces

References

• [1] Majeed, R. N.,“C ̌ech fuzzy soft closure spaces”, International Journal of Fuzzy System Applications, 7(2): 62-74, (2018).
• [2] Zadeh, L. A., “Fuzzy sets”, Information and Control, 8: 338-353, (1965).
• [3] Molodtsov, D. A., “Soft set theory first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
• [4] Maji, P. K., Biswas, R. and Roy, A. R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9(3): 589-602, (2001).
• [5] Tanay, B. and Kandemir, M. B., “Topological structures of fuzzy soft sets”, Computers and Mathematics with Applications, 61: 412-418, (2011).
• [6] C ̆ech, E., Topological spaces, Inter Science Publishers, John Wiley and Sons, New York, (1966).
• [7] Mashhour, A. S. and Ghanim, M. H., “Fuzzy closure spaces”, Journal of Mathematical Analysis and Applications, 106: 154-170, (1985).
• [8] Gowri, R. and Jegadeesan, G., “On soft C ̆ech closure spaces”, International Journal of Mathematics Trends and Technology, 9(2): 122-127, (2014).
• [9] Krishnaveni, J. and Sekar, C., “C ̆ech Soft Closure Spaces”, International Journal of Mathematical Trends and Technology, 6: 123-135, (2014).
• [10] Majeed, R. N. and Maibed, L.H., “Some structures of C ̌ech fuzzy soft closure spaces”, Journal of engineering and applied sciences, Accepted.
• [11] Roy, S. and Samanta, T. K., “A note on fuzzy soft topological spaces”, Annals of Fuzzy Mathematics and Informatics, 3(2): 305-311, (2012).
• [12] Varol, B. P. and Aygu ̈n, H., “Fuzzy soft Topology”, Hacettepe Journal of Mathematics and Statistics, 41(2): 407-419, (2012).
• [13] Mahanta, J. and Das, P.K., “Results on fuzzy soft topological spaces”, arXiv:1203.0634v, (2012).
• [14] Atmaca, S. and Zorlutuna, I ̇., “On fuzzy soft topological spaces”, Annals of Fuzzy Mathematics and Informatics, 5(2): 377-386, (2013).
• [15] Mishra, S. and Srivastava, R., “Hausdorff fuzzy soft topological spaces”, Annals of Fuzzy Mathematics and Informatics, 9(2): 247-260, (2015).