Measuring the confusion between two qualitative values organized in hierarchies

Sometimes, qualitative values can be arranged in a hierarchy, a tree with certain properties. Hierarchies allow the definitions of following constructs: the confusion CONF(r, s) in using qualitative value r instead of the intended or correct value s (such as using ‘umbrella’ when ‘raincoat’ was intended); a predicate P that holds for object o within confusion ε, written Pε(o); the closeness of an object to a predicate (closeness of fit); how close or similar two objects are; predicate P(o), where the total (cumulative) error produced by object o is at most ε. The hierarchy used represents how close two qualitative values are, as regarded by the user. The hierarchy provides the context against which confusions are measured. Several applications and examples are given or mentioned.