Conceptual Data Warehouse Design - Data Warehouse Systems: Design and Implementation - page 90

represented by the dimensions. For example, the Sales fact in Fig. 4.2 includes
the measures Quantity , UnitPrice , Discount , SalesAmount , Freight ,and Net-
Amount . The identifier attributes of the levels involved in a fact indicate the
granularity of the measures, that is, the level of detail at which measures are
represented.
Measures are aggregated along dimensions when performing roll-up oper-
ations. As shown in Fig. 4.1 d, the aggregation function associated with
a measure can be specified next to the measure name, where the SUM
aggregation function is assumed by default. In Chap. 3 , we classified measures
as additive , semiadditive ,or nonadditive .AsshowninFig. 4.1 e, we
assume by default that measures are additive, that is, they can be summarized
along all dimensions. For semiadditive and nonadditive measures, we include
the symbols '+!' and '+', respectively. For example, in Fig. 4.2 the measures
Quantity and UnitPrice are, respectively, additive and semiadditive measures.
Further, measures and level attributes may be derived ,wheretheyare
calculated on the basis of other measures or attributes in the schema. We use
the symbol '/' for indicating derived measures and attributes. For example,
in Fig. 4.2 , the measure NetAmount is derived.
A hierarchy comprises several related levels, as in Fig. 4.1 b. Given two
related levels of a hierarchy, the lower level is called the child and the higher
level is called the parent . Thus, the relationships composing hierarchies
are called parent-child relationships .The cardinalities in parent-child
relationships, as shown in Fig. 4.1 c, indicate the minimum and the maximum
number of members in one level that can be related to a member in another
level. For example, in Fig. 4.2 , the child level Product is related to the
parent level Category with a one-to-many cardinality, which means that every
product belongs to only one category and that each category can have many
products.
A dimension may contain several hierarchies, each one expressing a par-
ticular criterion used for analysis purposes; thus, we include the hierarchy
name (Fig. 4.1 f) to differentiate them. If a single level contains attributes
forming a hierarchy, such as the attributes City , Region ,and Country in the
Employee dimension in Fig. 4.2 , this means that the user is not interested in
employing this hierarchy for aggregation purposes.
Levels in a hierarchy are used to analyze data at various granularities or
levels of detail. For example, the Product level contains specific information
about products, while the Category level may be used to see these products
from the more general perspective of the categories to which they belong. The
level in a hierarchy that contains the most detailed data is called the leaf
level . The name of the leaf level defines the dimension name, except for the
case where the same level participates several times in a fact, in which case
the role name defines the dimension name. These are called role-playing
dimensions . The level in a hierarchy representing the most general data is
called the root level . It is usual (but not mandatory) to represent the root
of a hierarchy using a distinguished level called All , which contains a single