On the lattice of intervals and rough sets

Summary. Rough sets, developed by Pawlak, are important tool to descri-be situation of incomplete or partially unknown information. On of the algebraic models is the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, we concentrate here rather at the model with the pair of two defi-nable sets. Hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [6], is also a step towards the formalization of the algebraic theory of rough sets, as in [?] or [?]