  Approximate functional dependencies (AFDs) are functional dependencies (FDs)
that "almost" hold in a relation. While various measures have been proposed to
quantify the level to which an FD holds approximately, they are difficult to
compare and it is unclear which measure is preferable when one needs to
discover FDs in real-world data, i.e., data that only approximately satisfies
the FD. In response, this paper formally and qualitatively compares AFD
measures. We obtain a formal comparison through a novel presentation of
measures in terms of Shannon and logical entropy. Qualitatively, we perform a
sensitivity analysis w.r.t. structural properties of input relations and
quantitatively study the effectiveness of AFD measures for ranking AFDs on real
world data. Based on this analysis, we give clear recommendations for the AFD
measures to use in practice.
