Database Reference
In-Depth Information
While considering real world objects another very important consideration that needs to be taken
into account is the inherent fuzziness in the data instances. Often the data we have to manage are far
from being precise and certain. Indeed, the attribute value of an item may be completely unknown or
partially known (a probability distribution is known on the possible values of attribute, for example).
Besides an attribute may be irrelevant for some of the considered items; moreover, we may not know
whether the values does not exist or is simply unknown. In such circumstances fuzzy relations are in-
corporated in the database. Integration of fuzziness in database provides means of representing, storing,
and manipulating imprecise and uncertain information. Since our knowledge of the real world is often
imperfect, one's ability to create databases of integrity poses a great challenge. To maintain the integrity
of database in situations where knowledge of the real world is imperfect, one may either restrict the
model of database to the portion about which only perfect information is available leading to the loss of
valuable information, keeping relevant data unexplored, unanswered queries, unsatisfied user requests
and resulting in degraded quality of information delivery. To overcome the aforesaid hazards, formal-
ism has been suggested that allow the representation, storage, retrieval and manipulation of uncertain
information. In this research work the term FUZZY is used as a generalized term implying imprecision,
uncertainty, partial knowledge, vagueness and ambiguity.
Fuzzy relations have been treated by Kaufman (1975) and Zadeh (1965). A considerable work on
solving the equality problem among fuzzy data values are in the literature. Buckles and Petry (1983),
and Prede and Testamale (1984) introduced the concept of similarity measure to test the two domains
for equality of fuzzy data values. Rundensteiner (1989) introduced a new equality measure termed as
resemblance relation. The concept behind the resemblance relation and proximity relation are somewhat
similar and has been exploited by Raju and Majumdar (1986). A fuzzy probabilistic relational data
model is proposed by Zhang, Laun and Meng (1997) to integrate local fuzzy relational databases into a
fuzzy multidatabase system by identifying and resolving new types of conflicts in local fuzzy database
schemas. Another approach in (Ma, Zhang and Ma, 2000) addressed the fuzzy multidatabase systems
for identifying and resolving the involved conflicts in their schema integration.
FUZZY TUPLE SOURCE RELATIONAL DATA MODEL
Definition:
Let
U
be a universe of discourse. A set
F
is a fuzzy set of
U
if there is a membership func-
tion
m
F
®
0 1
, which associates with each element
u
∧
U
a membership value
m
F
( )
in the interval
[0,1]. The membership value
m
F
( )
for each
u
∧
U
represents the grade of membership of the element
u
in the fuzzy set
F
.
F
may be represented by
F
:
U
[ ,
]
{
( ) /
u
u u U
|
}
=
m
∈
.
F
Definition:
Let
U
*
= × × ×
1
U U
2
be the cartesian product of n universes and
A A
U
n
,
,
,
be
A
n
1
2
fuzzy set in
U U
,
,
,
respectively. Then the cartesian product
A A
U
n
´ ´ ´
is defined to be a fuzzy
A
n
1
2
1
f
(
)
subset (denoted byÍ
) of
U U
´ ´ ´
, with
m
)
, Where
U
n
(
u u
,
,
,
u
) min
=
m
(
u
),
m
(
u
),
,
m
(
u
A A
× × ×
A
1
2
n
A
1
A
2
A
n
1
1
2
n
1
2
n
1 2
. An
n
-ary fuzzy relation
R
in
U*
is a relation that is characterized by a
n
-variate
membership function ranging over
U*
, that is,
m
R
u U i
∈
,
=
,
,
,
n
i
i
:
U
*
®
0 1
.
[ ,
]
