Rasha MAJEED, Lina MAIBED

Lower Separation Axioms in ? ̌ech Fuzzy Soft Closure Spaces

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, ?? (? = 0,1,2), semi- (respectively, pseudo and Uryshon) ?2 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 ??, ? = 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.

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[1] Zadeh, L. A., “Fuzzy sets”, Information and Control, 8: 338-353, (1965).
[2] Molodtsov, D. A., “Soft set theory first results”, Computers and Mathematics with Applications, 37: 19-31, (1999).
[3] Maji, P. K., Biswas, R. and Roy, A. R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9(3): 589602, (2001).
[4] Tanay, B. and Kandemir, M. B., “Topological structures of fuzzy soft sets”, Computers and Mathematics with Applications, 61: 412-418, (2011).
[5] ? ̆ech, E., Topological spaces, Inter Science Publishers, John Wiley and Sons, New York, (1966).
[6] Mashhour, A. S. and Ghanim, M. H., “Fuzzy closure spaces”, Journal of Mathematical Analysis and Applications, 106: 154-170, (1985).
[7] Gowri, R. and Jegadeesan, G., “On soft ? ̆ech closure spaces”, International Journal of Mathematics Trends and Technology, 9(2): 122-127, (2014).
[8] Krishnaveni, J. and Sekar, C., “? ̆ech Soft Closure Spaces”, International Journal of Mathematical Trends and Technology, 6: 123-135, (2014).
[9] Majeed, R. N.,“C ̌ech fuzzy soft closure spaces”, International Journal of Fuzzy System Applications, 7(2): 62-74, (2018).
[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 Aygün, 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, İ., “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).