Database Reference
In-Depth Information
a
si
Q
max
is absolute
Φ
max
=
(13)
a
/
b
si
Q
max
is relative
with
a
and
b
being the same values defi ned in previous case. To compute the warning area
is easy, because we must use δ
min
and δ
max
.
Fuzzy Degrees
Sometimes, fuzzy information is expressed with a degree. The domain of these degrees
is usually limited to the interval [0,1], but other values can be allowed, as for example pos-
sibility distributions. We will use these degrees for measuring certain fuzzy components in
aggregations and specializations.
Besides, the meaning of those degrees varies. Depending on this meaning the treatment
of the data will be possibly different. The most important meanings of the grades are the
following, and in Galindo (1999) and Galindo et al. (2001a), we found some authors who
used these different meanings:
fulfi lment
(a property can be complied with a certain degree
between two ends),
membership
(which measures the level of membership or ownership
of an object to a set),
importance
(different objects can have different importance, so that
there are objects more important than others) and
uncertainty
(the degree expresses the
security with which we know a specifi c data).
FUZZY AGGREGATIONS
This approach is an extension of the fi rst level by Zvieli and Chen (1986) applied to
aggregations. De Miguel et al. (1999) defi ne an aggregation like an entity which is composed
of one set of different elements. They defi ne two kinds of aggregations and we add a fuzzy
degree to each element:
1.
Fuzzy aggregation of attributes:
This is the most common type of aggregation and it
expresses that an entity is a set of attributes. Fuzzy aggregation of attributes is repre-
sented using circles with dashed lines for the graded attributes, indicating the degree
of each one with: G
m
=<degree>, where
m
is the meaning of this degree.
2.
Fuzzy aggregation of entities:
This aggregation expresses that each instance of an ag-
gregated entity is composed of others' instances of others' entities. This aggregation is
denoted by a rhombus with dashed line close to the aggregated entity. The other entities
join the rhombus with a line labeled with: G
m
=<degree>, where
m
is the meaning of
this degree.
Example 2.
Figure 4 models that a car has some attributes: serial number (the primary
key), color, year, potency, etc. On the other hand, a car is composed of a chassis, an engine,
radio and specialized computer, cylinder and other entities. Some of these elements (attri-
butes and entities) have a membership degree to the model.
Thus, if we want a detailed model we can use all elements, but if we do not need
such a detailed model we can get only elements with membership degree greater to 0.7,
