Information Technology Reference
In-Depth Information
Remark 1.3.4 It should be noticed that what has been presented is sufficient but not
necessary for the representation of
μ PandQ and
μ Por Q b means of
μ P and
μ Q .
P
) ,
Given P , if with M for medium , MP
=
Not P
and
Not aP
=
and
(
aP
with a negation function N for not , and a symmetry A for the opposite, and
for
and , results
μ MP ( x ) = μ P and ( aP ) ( x ) = μ P ( x ) μ ( aP ) ( x ) = N P ( x )) N P ( A ( x ))),
for all x in X .
1.4 Qualified, Modified, and Constrained Predicates
1.4.1 Qualified Predicates
Let P be a predicate on X , with L-degree
μ P
:
X
L , and
˄
a predicate on
μ P (
X
)
L , with L-degree
μ ˄ : μ P (
X
)
L . Suppose
˄ , and consider the
qualified predicate ' P is
˄
',
' x is
(
P is
˄ )
'
:=
x is P is
˄ ,
∅ = Pis ˄ P . On these conditions,
provided
μ Pis ˄ = μ ˄ μ P
is an L-degree for ' P is
˄
'in X , since:
x
Pis ˄
y
x
P y
μ P (
x
) μ P (
y
) μ P (
x
) ˄ μ P (
y
)
μ ˄ P (
x
)) μ ˄ P (
y
)),
that is,
˄ μ P )(
x
) ˄ μ P )(
y
).
= 1 , and
For example, with L
=[
0
,
1
]
, P
=
small in
[
0
,
10
]
, with
P
x
μ P (
x
) =
1
10 ,if
˄ =
large in
[
0
,
1
]
is with
˄ =
, and
0
,
if
0
x
0
.
5
μ ˄ (
x
) =
1
,
if
0
.
5
x
1
,
it results
0
,
if
5
x
<
10
μ ˄ μ P (
x
) =
1
,
if
0
x
<
5
,
that allow the interpretation of small is large as less than five .
 
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