  The generalization of the Morse theory presented by Goresky and MacPherson is
a landmark that divided completely the topological and geo\-me\-tri\-cal study
of singular spaces. In this work, we consider $(X,0)$ a germ at $0$ of toric
variety and non-degenerate function-germs $f,g : (X,0) \to (\mathbb{C},0)$, and
we prove that the difference of the Brasselet numbers ${\rm B}_{f,X}(0)$ and
${\rm B}_{f,X\cap g^{-1}(0)}(0)$ is related with the number of Morse critical
points {on the regular part of the Milnor fiber} of $f$ appearing in a
morsefication of $g$, even in the case where $g$ has a critical locus with
arbitrary dimension. This result connects topological and geometric properties
and allows us to determine many interesting formulae, mainly in therms of the
combinatorial information of the toric varieties.
