Similarity metrics: A formal unification of cardinal and non-cardinal similarity measures

In [9] we introduced a formal framework for constructing ordinal similarity measures, and suggested how this might also be applied to cardinal measures. In this paper we will place this approach in a more general framework, called similarity metrics. In this framework, ordinal similarity metrics (where comparison returns a boolean value) can be combined with cardinal metrics (returning a numeric value) and, indeed, with metrics returning values of other types, to produce new metrics.