# SUPRA FUZZY CONVERGENCE OF FUZZY FILTERS

• Ramadan, A.A. (Department of Mathematics Faculty of Science Al-Qassem University) ;
• El-Latif, A.A. Abd (Department of Mathematics Faculty of Science Beni-Suef University)
• Published : 2008.05.31

#### Abstract

We introduce and study the notions of supra fuzzy convergence of fuzzy filters, $s{\gamma}$-fuzzy open (closed) sets, $s{\gamma}(/TEX>$s{\gamma}^*)$-fuzzy continuous and$s{\gamma}\$-fuzzy open mapping. Also. we investigate some of fundamental properties of these notions.

#### References

1. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190 https://doi.org/10.1016/0022-247X(68)90057-7
2. K. C. Chattopadhyay, R. N. Hazra, and S. K. Samanta, Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 49 (1992), no. 2, 237-242 https://doi.org/10.1016/0165-0114(92)90329-3
3. K. C. Chattopadhyay and S. K. Samanta, Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness, Fuzzy Sets and Systems 54 (1993), no. 2, 207-212 https://doi.org/10.1016/0165-0114(93)90277-O
4. M. Demirci, Neighborhood structures of smooth topological spaces, Fuzzy Sets and Systems 92 (1997), no. 1, 123-128 https://doi.org/10.1016/S0165-0114(96)00132-7
5. M. H. Ghanim, O. A. Tantawy, and F. M. Selim, Gradation of supra-openness, Fuzzy Sets and Systems 109 (2000), no. 2, 245-250 https://doi.org/10.1016/S0165-0114(97)00342-4
6. M. Guloglu and D. Coker, Convergence in I-fuzzy topological spaces, Fuzzy Sets and Systems 151 (2005), no. 3, 615-623 https://doi.org/10.1016/j.fss.2004.06.016
7. U. Hohle and A. P. Sostak, A general theory of fuzzy topological spaces, Fuzzy Sets and Systems 73 (1995), no. 1, 131-149 https://doi.org/10.1016/0165-0114(94)00368-H
8. Y. C. Kim, r-fuzzy semi-open sets in fuzzy bitopological spaces, Far East J. Math. Sci. (FJMS) 2000, Special Volume, Part II, 221-236
9. Y. C. Kim, Initial L-fuzzy closure spaces, Fuzzy Sets and Systems 133 (2003), no. 3, 277-297 https://doi.org/10.1016/S0165-0114(02)00224-5
10. P. M. Pu and Y. M. Liu, Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), no. 2, 571-599 https://doi.org/10.1016/0022-247X(80)90048-7
11. A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), no. 3, 371-375 https://doi.org/10.1016/0165-0114(92)90352-5
12. A. A. Ramadan, Smooth filter structures, J. Fuzzy Math. 5 (1997), no. 2, 297-308
13. A. A. Ramadan, M. A. Abd El-Satter, and Y. C. Kim, Some properties of smooth filters, J. Fuzzy Math. 11 (2003), no. 2, 341-354
14. A. P. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (2) Suppl. No. 11 (1985), 89-103
15. A. P. Sostak, On the neighborhood structure of fuzzy topological spaces, Zb. Rad. No. 4 (1990), 7-14
16. A. P. Sostak, Basic structures of fuzzy topology, J. Math. Sci. 78 (1996), no. 6, 662-701 https://doi.org/10.1007/BF02363065