Multiplicity Not Cardinality

12 August 2003

When data modeling methods talk about relationships, they use the term cardinality to indicate how many entities may be linked together. So you might have a relationship between order and customer and say that the cardinality of the relationship is one-to-many. Or you might hear that the cardinality of customers for an order is 0-to-many.

UML avoids the term cardinality preferring to use multiplicity. Often people with a data modeling background are surprised at this since cardinality has been so widely used in data modeling circles.

The reason for the change is that the dictionary definition of cardinality is "the number of elements in a particular set or other grouping" (OED). According to this the data modeling usage is actually wrong. In the excellent UML Reference Manual, Rumbaugh defines multiplicity as "A specification of the range of allowable cardinality values - the size - that a set may assume". The UML uses multiplicity in various places, for a property (association or attribute) and also to show the multiplicity of parts in a composite structure. It's formally defined as a lower and upper bound. An association (the UML equivalent to a relationship in data modeling circles) has a multiplicity for each direction.