  Intuitively, the concept of similarity is the notion to measure an inexact
matching between two entities of the same reference set. The notions of
similarity and its close relative dissimilarity are widely used in many fields
of Artificial Intelligence. Yet they have many different and often partial
definitions or properties, usually restricted to one field of application and
thus incompatible with other uses. This paper contributes to the design and
understanding of similarity and dissimilarity measures for Artificial
Intelligence. A formal dual definition for each concept is proposed, joined
with a set of fundamental properties. The behavior of the properties under
several transformations is studied and revealed as an important matter to bear
in mind. We also develop several practical examples that work out the proposed
approach.
