The smooth closure and smooth interior of a fuzzy set w.r.t. a smooth topology were defined by Gayyar et al. (1994), and some relations between a few types of compactness were established in the presence of strong restrictions. In this paper, by constructing new definitions of smooth closure and smooth interior which have more desirable properties than those of Gayyar et al. (1994), we prove that several hypothesis in the results of Gayyar et al. (1994) can be weakened and show that the relations which hold between various types of compactness in fuzzy topological spaces in Chang's sense (CFTS for short) (Di Concilio and Gerla, 1984; Haydar Es, 1987) can be extended to smooth topological spaces. (C) 1997 Published by Elsevier Science B.V.