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μ
old
as
Analogously, a person in the twenties could design
Remark 1.1.10
There are different models for the uses of the same predicate
P
in
X
,
and such uses are reflected in the corresponding models
X
. It is because of
this that it is actually important the process of designing the membership functions.
μ
P
in
[
,
]
0
1
Example 1.1.11
Analogously to the case of
big
, the predicate
A
5
=
around five
in
[
0
,
10
]
, can have non-linear but quadratic models, as the one given by
⊧
⊨
0
,
if
x
∈[
0
,
4
]∪[
6
,
10
]
2
μ
A
5
(
x
)
=
(
x
−
4
)
,
if
x
∈[
4
,
5
]
⊩
2
(
6
−
x
)
if
x
∈[
5
,
6
]
,
whose graphics is
Remark 1.1.12
μ
P
, at each
particular case the meaning of
P
should be well captured to not represent it by a
mistaken function that will translate a different use of the predicate.
Since each
P
in a set
X
can have different degrees
Remark 1.1.13
Given
μ
P
, and the
L
−
set
P
∼
, the degree is also called the
membership
function
of the
L
-set. At this respect,
•
x
∈
ʱ
P
∼
, is classically written
x
∈
P
∼
•
x
∈
ˉ
P
∼
, is classically written
x
∈
P
∼
.
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