Database Reference
In-Depth Information
0
if
u
≤
u
1
2
m
(
u u
,
)
=
m
(
u u
,
)
otherwise
.
GT
1
2
P
1
2
1
Definition:
Let
P
2
is a proximity relation defined over a universe of discourse
U
. The fuzzy rela-
tional operator
LT
is defined to be a fuzzy subset of
U
×
U
, where
μ
LT
satisfies the following properties
∀
u u
,
∈
U
:
1
2
0
if
u
≥
u
1
2
m
(
u u
,
)
=
LT
1
2
m
(
u u
,
)
otherwise
.
P
1
2
1
Membership functions of fuzzy relations `NOT EQUAL' (
NEQ
), `GREATER THAN OR EQUAL'
(
GOE
) and `LESS THAN OR EQUAL' (
LOE
) can be defined based on that of
EQ
,
GT
and
LT
as follows:
m
m
m
(
u u
u u
u u
,
)
=
=
=
[
1
−
u u
m
(
u u
,
)]
NEQ
1
2
EQ
1
2
(
,
)
max[
(
,
),
(
u u
,
)]
m
m
GOE
1
2
GT
1
2
EQ
1
2
(
,
)
min[
m
(
u u
,
),
m
(
u u
,
)]
LOE
1
2
LT
1
2
EQ
1
2
Integration of Fuzzy Relational Databases
The merge operation defined in (Lim, Chiang and Cao, 1999) can be used to integrate local fuzzy rela-
tional databases into a fuzzy relational multidatabase of type-2 as given below.
In deriving level-0 global fuzzy relations from export fuzzy relations, we assume that each global
fuzzy relation is formed by one or none export fuzzy relation from each export fuzzy relational database.
This assumption is reasonable since the export fuzzy relational database should have a schema compat-
ibility with that of integrated fuzzy relational database. To combine the export fuzzy relations of a global
fuzzy relation, we need a merge operation.
Let
DB
1
, ,
be n export fuzzy relational databases, and let
L
ij
be a fuzzy relation in
DB
i
. The
fuzzy relation
L
ij
is a component of the global fuzzy relation
G
j
which is derived from
L
DB
n
,
,
by
L
1
j
nj
G
1
.
Definition:
(merge operation) Let
DB
be the set of all export fuzzy relational databases,
DB
=
merge L
(
,
,
L
)
j
j
nj
1
,
,
DB
n
1
, ,
respectively. They all correspond to the
same global fuzzy relation
G
j
.
L
ij
is empty if no export fuzzy relation from
DB
i
correspond to
G
j
. Let
A Attr L
. Let
L
,
,
be export fuzzy relations from
DB
L
DB
n
1
j
nj
=
(
)
∪ ∪
Attr L
(
)
, then
1
j
nj
merge L
(
,
,
L
)
=
extends L A DB
(
,
,
)
∪ ∪
extends L A DB
(
,
,
)
,
1
j
nj
1
j
1
nj
n
where
extends
(
L
ij
,
A
,
B
i
) augments records in
L
ij
with Null values for attributes in
A
that are not found in
L
ij
, and
DB
i
for the source attribute.
