Database Reference
In-Depth Information
Basically, one can follow the two general formal approaches to the querying: the
relational algebra
and the
relational calculus.
However, for our purposes the exact form of queries is not that important
as we focus on the condition part of queries.
A
fuzzy set F
in the universe
U
is characterized by a membership function
→
m
F
:
U
0 1
,
(2)
where for each element
x
∧
U
,
μF
(
x
) denotes the membership grade or extent to which
x
belongs to
F.
Fuzzy sets make it possible to represent vague concepts, like “
tall
man” by reflecting the graduality
of such a concept.
Fundamentals of Flexible Fuzzy Querying of Databases
The basic idea behind the concept of flexible fuzzy queries is the use of natural language (fuzzy) terms
in their conditions. The main approaches include: modelling linguistic terms in queries using fuzzy logic
(Tahani, 1977); enhancements of the fuzzy query formalism with flexible aggregation operators (Kacprzyk
& Ziółkowski, 1986; Kacprzyk, Zadrożny & Ziółkowski, 1989; Bosc & Pivert, 1993; Dubois & Prade,
1997), and embedding fuzzy constructs in the syntax of the standard SQL (Bosc & Pivert, 1992a; Bosc
& Pivert, 1992b; Umano & Fukami, 1994; Bosc & Pivert, 1995; Kacprzyk & Zadrożny, 1995; Galindo
et al., 1998; Bosc, 1999; Galindo, Urrutia & Piattini, 2006; De Tré et al., 2006).
Fuzzy Preferences Inside Query Conditions
The first proposal to use fuzzy logic to improve the flexibility of crisp database queries is due to Tahani
(1977) who proposed, within SQL to use vague linguistic terms as, e.g., “high” and “young” in “WHERE
salary =
HIGH
AND age =
YOUNG
”, represented by fuzzy sets. Then, for a tuple
t
and a simple (elemen-
tary) condition
q
of type
A = l
, where
A
is an attribute (e.g., “age”) and
l
is a linguistic (fuzzy) term (e.g.,
“YOUNG”), the value of the
matching degree,g
, is:
(
)
=
( )
γ
q t
,
µ
x
(3)
l
where
x
is
t
[
A
], i.e. the value of tuple
t
for attribute
A
and
m
l
is the membership function of the fuzzy
set representing the linguistic term
l
. The
g
for complex conditions, as, e.g., “age =
YOUNG
AND (sal-
ary =
HIGH
OR empyear =
RECENT
)” is obtained using the fuzzy logical connectives, i.e.,
(
)
(
)
=
(
)
(
)
g
p
∧
q t
,
min
g
p t
,
,
g
q t
,
(4)
(
)
=
(
(
)
(
)
)
g
p
∨
q t
,
max
g
p t
,
,
g
q t
,
(5)
(
)
= −
(
)
g
q t
,
1
g
q t
,
(6)
