  We present a novel approach for data set scaling based on scale-measures from
formal concept analysis, i.e., continuous maps between closure systems, and
derive a canonical representation. Moreover, we prove said scale-measures are
lattice ordered with respect to the closure systems. This enables exploring the
set of scale-measures through by the use of meet and join operations.
Furthermore we show that the lattice of scale-measures is isomorphic to the
lattice of sub-closure systems that arises from the original data. Finally, we
provide another representation of scale-measures using propositional logic in
terms of data set features. Our theoretical findings are discussed by means of
examples.
