# SOME RESULTS ON INTUITIONISTIC FUZZY TOPOLOGICAL SPACES DEFINED BY INTUITIONISTIC GRADATION OF OPENNESS

MIN WON KEUN;PARK CHUN-KEE

• Published : 2005.10.01
• 30 7

#### Abstract

In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

#### Keywords

intuitionistic fuzzy sets;intuitionistic gradation of open­ness;weakly gp-map;gp-open map;intuitionistic fuzzy cover;intuitionistic fuzzy compact;nearly intuitionistic fuzzy compact;almost intuitionistic fuzzy compact

#### 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), 237-242 https://doi.org/10.1016/0165-0114(92)90329-3
3. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and System 88 (1997), 81-89 https://doi.org/10.1016/S0165-0114(96)00076-0
4. M. Demirci, On several types of compactness in smooth topological spaces, Fuzzy Sets and Systems 90 (1997), 83-88 https://doi.org/10.1016/S0165-0114(96)00121-2
5. M. K. El Gayyar, E. E. Kerre, and A. A. Ramadan, Almost compactness and near compactness in smooth topological spaces, Fuzzy Sets and Systems 62 (1994), 193-202 https://doi.org/10.1016/0165-0114(94)90059-0
6. R. N. Hazra, S. K. Samanta, and K. C. Chattopadhyay, Fuzzy topology redefined, Fuzzy Sets and Systems 45 (1992), 79-82 https://doi.org/10.1016/0165-0114(92)90093-J
7. T. K. Mondal and S. K. Samanta, On intuition is tic gradation of openness, Fuzzy Sets and Systems 131 (2002), 323-336 https://doi.org/10.1016/S0165-0114(01)00235-4
8. A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), 371-375 https://doi.org/10.1016/0165-0114(92)90352-5
9. L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X
10. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and System 20 (1986), no. 1, 87-96 https://doi.org/10.1016/S0165-0114(86)80034-3
11. M. Demirci, Three topological structures of smooth topological spaces, Fuzzy Sets and Systems 101 (1999), 185-190 https://doi.org/10.1016/S0165-0114(97)00117-6