  Since the theory of rough sets was introduced by Zdzislaw Pawlak, several
approaches have been proposed to combine rough set theory with fuzzy set
theory. In this paper, we examine one of these approaches, namely fuzzy rough
sets with crisp reference sets, from a lattice-theoretic point of view. We
connect the lower and upper approximations of a fuzzy relation $R$ to the
approximations of the core and support of $R$. We also show that the lattice of
fuzzy rough sets corresponding to a fuzzy equivalence relation $R$ and the
crisp subsets of its universe is isomorphic to the lattice of rough sets for
the (crisp) equivalence relation $E$, where $E$ is the core of $R$. We
establish a connection between the exact (fuzzy) sets of $R$ and the exact
(crisp) sets of the support of $R$.
