Database Reference
In-Depth Information
e.g.,
“
Most
(
Q
) of the
important
(
B
) conditions (
y
's) are
satisfied
(
F
)”.
(15)
The problem is to find truth(
Qy's
are
F
) or truth(
QBy's
are
F
)
,
respectively, knowing truth(y is
F
),
∧
y
∧
Y
. To this end property
F
and importance
B
are represented by fuzzy sets in
Y
, and a (proportional,
nondecreasing) linguistic quantifier
Q
is assumed to be a fuzzy set in [0,1] as, e.g.
1
for
for
for
x
≥
0 8
.
m
Q
( )
x
=
2
x
−
0 6
.
0 3
.
< <
≤
x
0 8
.
(16)
0
x
0 3
.
Then, due to Zadeh (1983)
∑
n
truth
(
Qy s
'
are
F
)
[
( )]
y
=
m
1
m
(17)
Q n
F
i
i
=
1
∑
n
∑
n
truth
(
QBy s
'
are
F
)
=
m
[
(
m
( )
y
∧
m
( )) /
y
m
( )]
y
(18)
Q
B
i
F
i
B
i
i
=
1
i
=
1
There is a lot of works on this topic studying various possible interpretations of linguistic quantifiers
for the flexible querying purposes; cf., e.g., (Bosc, Pivert & Lietrad, 2001; Bosc, Lietrad & Pivert, 2003;
Galindo, Urrutia & Piattini, 2006; Vila, Cubero, Medina & Pons, 1997).
The linguistic quantifier guided aggregation is also relevant for our further considerations concerning
data mining related extensions of flexible fuzzy querying discussed in what follows.
Towards Implementable Fuzzy Querying Systems
Among the best known approaches to an implementable fuzzy querying systems, one can mention:
SQL
f
(SQLfuzzy) (Bosc & Pivert, 1995), an extension of the SQL introducing linguistic (fuzzy) terms
wherever it makes sense, Galindo et al.'s (1998) FSQL (FuzzySQL), a more comprehensive approach,
along the lines of SQLf
f
and beyond, and FQUERY (FuzzyQUERY) for Access (Kacprzyk & Zadrożny,
1995), an implementation of a specific “fuzzy extension” of SQL for Microsoft Access®.
We will only present in more detail FQUERY for Access proposed in a series of papers by Kacprzyk
& Zadrożny starting with (Kacprzyk & Zadrożny, 1995). It is relevant for our discussion.
FQUERY for Access package is a result of a practical approach to flexible fuzzy querying. We first
identified the classes of linguistic terms most useful for the purposes of database querying. These resulted
in the following classification:
1. terms representing inherent imprecision of some queries' conditions, including:
a. numeric fuzzy values (e.g., “cheap”),
b. modifiers (e.g. “very” in “very cheap”),
c. fuzzy relations (e.g., “much greater than”),
d. fuzzy sets of scalar values (e.g., “well-developed countries”)
