  We introduce the concept of quasi-Lov\'asz extension as being a mapping
$f\colon I^n\to\R$ defined on a nonempty real interval $I$ containing the
origin and which can be factorized as
$f(x_1,...,x_n)=L(\phi(x_1),...,\phi(x_n))$, where $L$ is the Lov\'asz
extension of a pseudo-Boolean function $\psi\colon\{0,1\}^n\to\R$ (i.e., the
function $L\colon\R^n\to\R$ whose restriction to each simplex of the standard
triangulation of $[0,1]^n$ is the unique affine function which agrees with
$\psi$ at the vertices of this simplex) and $\phi\colon I\to\R$ is a
nondecreasing function vanishing at the origin. These functions appear
naturally within the scope of decision making under uncertainty since they
subsume overall preference functionals associated with discrete Choquet
integrals whose variables are transformed by a given utility function. To
axiomatize the class of quasi-Lov\'asz extensions, we propose generalizations
of properties used to characterize the Lov\'asz extensions, including a
comonotonic version of modularity and a natural relaxation of homogeneity. A
variant of the latter property enables us to axiomatize also the class of
symmetric quasi-Lov\'asz extensions, which are compositions of symmetric
Lov\'asz extensions with 1-place nondecreasing odd functions.
