Some recent results on Atanassov's intuitionistic fuzzy topological spaces

Abstract

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. D. Coker constructed the fundamental theory on intuitionistic fuzzy topological spaces, and D. Coker and other mathematicians studied compactness, connectedness, continuity, separation, convergence and paracompactness in intuitionistic fuzzy topological spaces. Finally, G.-J Wang and Y.Y. He showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropriate lattice L. Nevertheless, the results obtained by above authors are not redundant with other for ordinary fuzzy sense. Recently, Smarandache defined and studied neutrosophic sets (NSs) which generalize IFSs. This author defined also the notion of neutrosophic topology. We proved that neutrosophic topology does not generalize the concept of intuitionistic fuzzy topology.