Without directly involving the role of points, we introduce and study the notions of fuzzy $\lambda$-Hausdorff spaces and fuzzy $\mu$-compact spaces. A characterization of a map $f$ from a fuzzy $\lambda$-Hausdorff space $X$ to a fuzzy $\mu$-compact space $Y$, where $\lambda=f^{-1}(\mu)$, to be fuzzy $\lambda$-continuous is obtained, which puts such a characterization for the continuity of $f$ in ordinary topological setting, for fuzzy topological spaces. These notions and results have been formulated for intuitionistic fuzzy topological spaces also.