This paper proposes a generalization of Tsallis entropy and Tsallis relative
entropy and discusses some of their properties. This generalization is defined
with respect to a deformed exponential $\varphi$, which is the same used in
defining $\varphi$-families of probability distributions, and generalizes
important classes of distributions. The generalized relative entropy is then
shown to be a $\varphi$-divergence with some conditions and related to a
$\varphi$-family by a normalizing function. We determine necessary and
sufficient conditions for the generalized relative entropy so it satisfies the
partition inequality and jointly convexity. Further, such conditions are
fulfilled we derive the conditions about the inverse of the deformed
exponential $\varphi$ which results from such assumption. We also show the
Pinsker's inequality for the generalized relative entropy that provides a
relationship between the generalized relative entropy and the statistical
distance.