Database Reference
In-Depth Information
. . / mo
a
can still be propagated to the sub-queries for local relations corresponding
to
Dept.
Having performed
unions
of sub-fuzzy query results to construct the global relations
Dept
and
Emp
, a final
join
and
projection
of the global relations will be required as specified in the Global Fuzzy
query Residue.
T Fund EQ
2
66
Translation of Sub-Fuzzy Query Templates into Sub-Queries
Although the fuzzy query agents support Sub-queries on the export schemas which are compatible to
the global schema, translating Sub-fuzzy query templates into Sub-queries is still necessary for the fol-
lowing reasons:
a.
Missing Export Fuzzy Relations:
In our FTS relational model, a FTS relation may not always
have its corresponding export fuzzy relation in every export fuzzy schema. When a FTS relation
in the FROM clause of a Sub-fuzzy query template cannot be found in an export fuzzy schema,
no fuzzy Sub-fuzzy query will be generated for the corresponding fuzzy query agent.
b.
Missing Fuzzy Attributes:
Some attributes of FTS relation may not be found in the export fuzzy
schema. If any FTS relation attribute involved in a WHERE clause of a Sub-fuzzy query template
cannot be found in the export fuzzy schema defined upon a local fuzzy database, it is not required
to translate the Sub-fuzzy query template for the fuzzy query agent of the local fuzzy database.
However, a translated Sub-fuzzy query is still required for each fuzzy query agent, if the WHERE
clause involves an explicit check for Null values.
Correctness of FTS Relational Model
Although FTS relational data model is designed for representing global fuzzy relations, it is closely
related to the component export fuzzy relational databases due to existence of source attribute. It is;
therefore, appropriate to characterize the correctness of FTS relational data model by showing that the
FTS relational operations are consistent with the fuzzy relational operations on export fuzzy relations.
Henceforth, we call these fuzzy relational operations the export fuzzy relational operations. Neverthe-
less, for FTS relational operations that combine fuzzy tuples from different export fuzzy relational da-
tabases, i.e.
fs
fs
fs
fs
fs
and
it is not possible to show their consistency with respect
to the export fuzzy relational operations because these FTS relational operations offer fuzzy query ex-
pressiveness beyond that of the export fuzzy relational operations. Hence, we have shown the correctness
only for the FTS relational operations that can be mapped into export fuzzy relational operations.
any
,
any
,
any
,
any
,
any
,
DD
∪
∩
−
Definition: (Consistency of Global Fuzzy Relational Operations)
Let DB
1
,…,
DB
n
be n export fuzzy databases and merge
()
be integrating operation that integrates the
export fuzzy relations into global fuzzy relations. Then the global fuzzy relational operation OP
G
is
consistent with the export fuzzy relational operations OP
L
iff
∧
a one to one mapping (denoted by opMap)
from OP
G
to
(
OP
{
op
}),
,(
OP
{
op
})
(
),
∀
op
OP
È
È
such that ∀
L
∈
Rel DB
∈
G
(say, OP
G
L
f
L
m
f
ij
i
G
1
