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⊧
⊨
1
,
if 10
x
15
25
−
x
μ
C
(
x
)
=
,
if 15
x
25
10
⊩
0
,
if 25
x
50
.
Which one of the following linguistic labels:
cold, hot, warm, more or less cold,
more or less warm
, is the more adequate for the temperatures of 20, 21 and 22
ⓦ
C?
So
lution
. With
C
5
10
=
cold, it is
μ
C
(
20
)
=
=
0
.
5 and
μ
more or less C
(
20
)
=
√
0
.
5
=
0
.
71. To obtain
H
=
hot
, we can compute
μ
H
as the opposite of
μ
C
:
⊧
⊨
1
,
if 45
x
50
x
−
35
10
μ
H
(
x
)
=
μ
C
(
50
+
10
−
x
)
=
μ
C
(
60
−
x
)
=
,
if 35
x
45
⊩
0
,
if 10
x
35
graphically
By defining, as it is usual, warm
=
not cold and not hot, that is
μ
w
=
μ
cold
·
μ
hot
represented by min, and
by
N
0
,
with
·
μ
w
(
x
)
=
min
(
1
−
μ
cold
(
x
),
1
−
μ
hot
(
x
)),
for all
x
∈[
10
,
50
]
, it results
Then:
5
10
5
10
•
x
=
20
,
gives
μ
c
(
20
)
=
=
0
.
5,
μ
H
(
20
)
=
0,
μ
W
(
20
)
=
=
0
.
5,
4
10
6
10
•
x
=
21
,
gives
μ
c
(
21
)
=
=
0
.
4,
μ
H
(
21
)
=
0,
μ
W
(
21
)
=
=
0
.
6,
3
10
7
10
•
x
=
22
,
gives
μ
c
(
22
)
=
=
0
.
3,
μ
H
(
22
)
=
0,
μ
W
(
22
)
=
=
0
.
7,
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