Let $f$ be a piecewise affine concave function on $N_{\mathbb{R}}$.

1. (1)

   $f$ is an H-lattice concave function (respectively, a rational piecewise affine concave function) if and only if $f^{\vee}$ is a V-lattice concave function (respectively, a rational piecewise affine concave function).

2. (2)

   $\operatorname{rec}(f)$ is an H-lattice concave function if and only if $\operatorname{stab}(f)$ is a lattice polyhedron.