Multiplicity vs Cardinality

Simply put: a multiplicity is made up of a lower and an upper cardinality. A cardinality is how many elements are in a set. Thus, a multiplicity tells you the minimum and maximum allowed members of the set. They are not synonymous.

The simplest explanation would be to say:

Multiplicity = Cardinality + Participation

Cardinality: Denotes the maximum number of possible relationship occurrences in which a certain entity can participate in (in simple terms: at most).

Participation: Denotes if all or only some entity occurrences participate in a relationship (in simple terms: at least).

Ex:

Thank you for the question and answers above.

Really got confused with those terms this morning (coffee did not help).

Given the example below:

0-1 ---------- 1-*

Multiplicities:

First multiplicity, for the left entity: 0-1

Second multiplicity, for the right entity: 1-*

Cardinalities for the first multiplicity:

Lower cardinality: 0

Upper cardinality: 1

Cardinalities for the second multiplicity:

Lower cardinality: 1

Upper cardinality: *

Martin Fowler has talked about this subject on his website. Quoting :

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.

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