Database Reference
In-Depth Information
is represented by joining it with all of its superclasses by a single line with the inclusion
symbol. Another representation utilizes the intersection symbol inside a circle: Superclasses
are joined to that circle by a line and the subclass is joined to that circle using a single line
with the inclusion symbol.
Just as with union types, in this type of specialization it is possible to apply fuzzy
constraints in two ways:
1.
Fuzzy participation constraint in one or more superclasses:
This constraint restricts
the number of instances, in the intersection of any group of superclasses, which
belong to the shared subclass. This is represented by an arc labeled with its fuzzy
quantifi er crossing the line which joins the selected superclass with the circle. This
fuzzy quantifi er would be relative. For example, with the quantifi er “almost all” on
a superclass the constraint expresses that: “almost all superclass elements belong to
the shared subclass”. Another option is to join two or more superclasses with the arc
indicating that the intersection of instances of those superclasses is constrained in
participation. This constraint allows the use of the fuzzy (min,max) notation indicating
the minimum and maximum number of instances which belong to the shared subclass
(using absolute or relative fuzzy quantifi ers). Generally, the participation constraint
is not useful, because one constraint on one superclass (or on several superclasses)
depends on the membership of its instances to the other superclasses (remember that
the subclass is a subset of the intersection).
2.
Fuzzy completeness constraints in the shared subclass (on the intersection of all
superclasses):
This constraint restricts the number of instances, in the intersection of
all superclasses, which belong to the shared subclass. This is represented by an arc
labeled with its fuzzy quantifi er, crossing the line which joins the shared subclass
with the circle. Normally, this fuzzy quantifi er will be relative. For example, with the
quantifi er “almost all” on the shared subclass the constraint expresses that: “almost
all elements of the intersection of all superclasses belong to the shared subclass”.
This constraint allows the use of the fuzzy (min,max) notation too, indicating the
minimum and maximum number of instances in the intersection (of all superclasses)
which belong to the shared subclass. Notice that this constraint is always referred to
as the intersection of all superclasses.
Example 11.
Let us consider an entity for Special Employees with its own attributes
(extra, payment, number of awards, motive...). A member of this shared subclass must be
engineer, chief and a permanent employee. Figure 11 depicts this model with the follow-
ing participation constraint: Almost all chiefs and permanent employees must be special
employees. It is interesting to note how this constraint enforces that almost all chiefs and
permanent employees must be engineers, too. It must be remembered that all special em-
ployees belong to Engineer superclass.
On the other hand, fuzzy completeness constraint establishes that approximately
half of employees who are engineers, chiefs and permanent employees must be special
employees.
In real models fuzzy constraints in the same specialization must be mixed with care.
Observe that a fuzzy participation constraint embracing all superclasses is a fuzzy complete-
ness constraint (both in union types and in intersection types).
