It is known that fuzziness within the concept of openness of a fuzzy
set in a Chang's fuzzy topological space (fts) is absent. In this
paper we introduce a gradation of openness for the open sets of a
Chang jts (X, $\mathcal{T}$) by means of a map $\sigma\;:\; I^{x}\longrightarrow I\left(I=\left[0,1\right]\right)$,
which is at the same time a fuzzy topology on X in Shostak 's sense.
Then, we will be able to avoid the fuzzy point concept, and to introduce
an adeguate theory for $\alpha$-neighbourhoods and $\alpha-T_{i}$
separation axioms which extend the usual ones in General Topology.
In particular, our $\alpha$-Hausdorff fuzzy space agrees with $\alpha${*}
-Rodabaugh Hausdorff fuzzy space when (X, $\mathcal{T}$) is interpreservative
or $\alpha$-locally minimal.
