Some recent results on Atanassov’s intuitionistic fuzzy topological spaces

We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set [1]. Some basic results on intuitionistic fuzzy sets were publised in [2,3], and the book [4] provides a comprehensive coverage of virtually all results until 1999 in the area of the theory and applications of intuitionistic fuzzy set. D. Çoker and M. Demirci [9] defined and studied the basic concept of intuitionistic fuzzy point, later D. Çoker [7, 8] constructed the fundamental theory on intuitionistic fuzzy topological spaces, and D. Çoker and others mathematicians [6, 10-27] studied compactness, connectedness, continuity, separation, convergence and paracompactness in intuitionistic fuzzy topological spaces. Finally, G.-J Wang and Y.Y. He [31] showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropriate lattice L. Nevertheless, the results obtained by the above authors are not redundants with other for the ordinary fuzzy sense. Recently, Smarandache [30] defined and studied neutrosophic sets (NSs) which generalize IFSs. This author defined also the notion of neutrosophic topology [28]. In [27] we proved that neutrosophic topology does not generalize the concept of intuitionistic fuzzy topology.