This paper discusses a variant theory for the Gorenstein flat
dimension. Actually, since it is not yet known whether the category
$\mathcal {GF}(R)$ of Gorenstein flat modules over a ring $R$ is
projectively resolving or not, it appears legitimate to seek
alternate ways of measuring the Gorenstein flat dimension of modules
which coincide with the usual one in the case where $\mathcal
{GF}(R)$ is projectively resolving, on the one hand, and present
nice behavior for an arbitrary ring $R$, on the other. In this
paper, we introduce and study one of these candidates
called the generalized Gorenstein flat dimension of a module $M$
and denoted by $\hbox{GGfd}_R(M)$ via considering exact sequences of
modules of finite flat dimension. The new entity stems naturally
from the very definition of Gorenstein flat modules. It turns out
that the generalized Gorenstein flat dimension enjoys nice behavior
in the general setting. First, for each $R$-module $M$, we prove
that $\hbox{GGfd} _R(M)=\hbox{Gid} _R(\mathop{\rm Hom} _{\mathbb{Z}} (M,\mathbb{Q}/\mathbb{Z}
) )$ whenever GGf$_R(M)$ is finite. Also, we show that $\mathcal
{GF}(R)$ is projectively resolving if and only if the Gorenstein
flat dimension and the generalized Gorenstein flat dimension
coincide. In particular, if $R$ is a right coherent ring, then
$\hbox{GGfd} _R(M)=\hbox{Gfd}_R(M)$ for any $R$-module $M$.
Moreover, the global
dimension associated to the generalized Gorenstein flat dimension,
called the generalized Gorenstein weak global dimension and denoted
by $\hbox{GG-wgldim}(R)$, turns out to be the best counterpart of the
classical weak global dimension in Gorenstein homological algebra.
In fact, it is left-right symmetric and it is related to the
cohomological invariants $\hbox{r-sfli}(R)$ and $\hbox{l-sfli}(R)$ by the formula
$$
\hbox{GG-wgldim}(R)=\max\{\hbox{r-sfli}(R),\hbox{l-sfli}(R)\}.
$$
