Let $\Lambda$ be a convex polyhedron and $f\in{\mathscr{D}}(\Lambda)$. We say that $f$ is an H-lattice (respectively V-lattice) function if it can be written as the difference of two H-lattice (respectively V-lattice) concave functions. We say that $f$ is a rational piecewise affine function if it is the difference of two rational piecewise affine concave functions.