  We study the fuzzy Potts model on a critical FK percolation in the plane,
which is obtained by coloring the clusters of the percolation model
independently at random. We show that under the assumption that this critical
FK percolation model converges to a conformally invariant scaling limit (which
is known to hold for the FK-Ising model), the obtained coloring converges to
variants of Conformal Loop Ensembles constructed, described and studied by
Miller, Sheffield and Werner. We also show, using discrete considerations that
the arm exponents for this coloring in the discrete model are identical to the
ones of the continuum model. Using the values of these arm exponents in the
continuum, we determine the arm exponents for the fuzzy Potts model.
