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Figure 5: Example 3. Fuzzy degrees in a specialization
or
partial
if this condition is not necessary. The inverse is not possible since, by defi nition,
partial
each member of a subclass must be a member of the superclass.
Total participation is represented by a double line joining the superclass with the
specialization circle, to which all the subclasses are joined using a single line. Partial par-
ticipation is represented by a single line.
For our fuzzy model, this constraint can be fuzzy using a relative fuzzy quantifi er
(mainly, although they can also be absolute fuzzy quantifi ers). This will be represented by
an arc labeled with its fuzzy quantifi er, crossing the line which joins the selected superclass
with the circle.
Example 4.
Let us consider the model in Figure 6 depicting an entity Employee which
is a superclass with two subclasses defi ned by the attribute Contract Type: Permanent and
Temporary. The arc and the relative fuzzy quantifi er “almost all” (Figure 2) indicate that
“Almost all employees must have a Permanent or Temporary contract, but other minority
contract types may exist (work experience, grants...)”. These other contract types are not in-
cluded in the model for various reasons (unknown types, types without own attributes...).
In the previous example, the specialization is disjointed (with a “d” in the circle) since
there cannot be an employee with various types of contracts. However, fuzzy completeness
constraints can also be applied to overlapping specializations (with an “o” in the circle) as
shown in the following example.
Example 5.
Let us consider an entity Employee which is a superclass with various
subclasses defi ning the abilities of the employees: Management Programmer, Systems
Programmer, Internet Programmer, Analyst, Graphic Designer, Accountant, etc., just like
Figure 7. The relative fuzzy quantifi er like “almost all” indicates that “Almost all employees
must have one or some of the abilities expressed in the subclasses.”
