Hierarchies measuring qualitative variables

Abstract

Qualitative variables take symbolic values, such as hot, shoe, Europe or France. Sometimes, the values may be arranged in layers or levels of detail. For instance, the variable place_of_origin takes as level-1 values European, African... as level-2 values French, German... as level-3 values Californian, Texan... The paper describes a hierarchy, a mathematical construct among these variables. The confusion resulting when using a value instead of another is defined, as well as the closeness to which object o fulfills predicate P. Other operations among and properties of hierarchical values are derived. Hierarchies are compared with ontologies. Hierarchies find use in measuring linguistic relatedness or similarity. Hierarchical variables abound and are commonly used, often with suggestive string values, without fully realizing or exploiting its properties. We deal with arbitrary hierarchies. Examples are given. © Springer-Verlag 2004.