Database Reference
In-Depth Information
Figure 8. An example of fuzzy partition defined for the attribute Salary
Tahani's Approach
Tahani (Tahani, 1977) was the first to propose a formal approach and architecture to deal with simple
fuzzy queries for crisp relational databases. More specifically, the author proposed to use in the query
condition fuzzy values instead of crisp ones. An example of a fuzzy query would be 'get employees
who are
young
and have a
reasonable
salary”. This query contains two fuzzy predicates 'Age =
young
'
and 'Salary =
reasonable
', where
young
and
reasonable
are words in natural language that express or
identify a fuzzy set (Figure 9).
Tahani's approach takes a relation
R
and a fuzzy query
q
over
R
as inputs and produces a fuzzy rela-
tion
R
q
, that is an ordinary relation in which each tuple
t
is associated with a matching degree
γ
q
within
[0, 1] interval. The value
γ
q
indicates the extent to which tuple
t
satisfies the fuzzy predicates involved
in the query
q
. The matching degree,
γ
q
, for each particular tuple
t
is calculated as follows. For a tuple
t
and a fuzzy query
q
with a simple fuzzy predicate
A = l
, where
A
is an attribute and
l
is a fuzzy set de-
fined on the attribute domain of
A
,
γ
A=l
is defined as follows:
γ
A=l
(t) = μ
l
(t.A)
where
t.A
is the value of tuple
t
on attribute
A
and
μ
l
is the membership function of the fuzzy set
l
.
For instance, consider the relation EmpDB in Table 4. The fuzzy relation corresponding to the fuzzy
predicate 'Age =
young
' (resp., 'Salary =
reasonable
') is shown in Table 5-(a) (resp., Table 5-(b)). Note
that when
γ
q
(t)
= 0, the tuple
t
does not belong to the fuzzy relation
R
q
any longer (for instance, tuple
#1 in Table 5-(a)).
The matching function
γ
for a complex fuzzy query with multiple fuzzy predicates is obtained by
applying the semantics of the fuzzy logical connectives, that are:
g
( ) min(
t
=
=
= −
g g
( ),
t
( ))
t
p
∧
p
p
p
1
2
1
2
g
t
max
g g
t
,
t
p
∨
p
p
p
1
2
1
2
g
t
1
g
t
¬
p
p
1
1
Figure 9. The fuzzy sets (values) young and reasonable
