The paper studies translation-invariant random sets X in \(R^ d\) which have the property that \(X\cap K\) (K is any convex body in \(R^ d)\) is with probability 1 an element of the convex ring. The main purpose is to extend the notions of densities of quermassintegrals which have been studied in G. Matheron, Random sets and integral geometry, (1975; Zbl 0321.60009) to general additive functionals defined for sets from the convex ring. The results of the theory of valuations of convex bodies are applied. A number of formulae for densities and expectations are obtained which resemble the classical formulae of integral geometry.