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and
•
μ
more or less cold
(
)
=
√
μ
c
(
20
20
)
=
0
.
71,
)
=
√
μ
W
(
μ
more or less
w
arm
(
20
20
)
=
0
.
71
•
μ
more or less
;
cold
(
21
)
=
0
.
63
, μ
more or less
;
w
arm
(
21
)
=
0
.
77,
•
μ
more or less
;
cold
(
22
)
=
0
.
55
, μ
more or less
;
w
arm
(
22
)
=
0
.
84.
Hence
•
The more adequate linguistic label for
x
20, cannot be decided but it could be
either 'not cold', or 'not warm'. Since, it is not hot at all, we can take 'not cold'.
=
•
For
x
=
21, is 'mol warm' (mol
=
more or less)
•
For
x
=
22,is'molwarm'
Example 2.2.48
On the age of a person
p
, it is known that
37
A
g
e
(
p
)
41
,
and neither
A
g
e
(
p
)
32, nor 43
A
g
e
(
p
)
. What can be said on the degree up to
which it could be
A
42?
Solution
. What is unknown is the variation of
A
g
e
(
p
)
=
35, and
A
g
e
(
p
)
=
between 32 and 37, as well
as between 41 and 43. Since Age varies continuously, we can suppose there are two
functions
g
e
(
p
)
:[
,
]ₒ[
,
]
, g
:[
,
]ₒ[
,
]
f
32
37
0
1
41
43
0
1
such that
f
(
32
)
=
0
,
f
(
37
)
=
1
, g(
41
)
=
1
, g(
43
)
=
0, with
f
strictly non-
decreasing, and
g
strictly decreasing. Then, we can define
μ
A
g
e
(
p
)
:[
0
,
100
]ₒ
[
0
,
1
]
,by
⊧
⊨
0
,
if
x
∈[
0
,
32
]∪[
43
,
100
]
1
,
if
x
∈[
37
,
41
]
μ
A
g
e
(
p
)
(
x
)
=
⊩
f
(
x
),
if
x
∈[
32
,
37
]
g(
),
∈[
,
]
x
if
x
41
43
and
μ
A
g
e
(
p
)
(
35
)
=
f
(
35
), μ
A
g
e
(
p
)
(
42
)
=
g(
42
)
. Graphically
f
()
g
Age
p
43
32
37 41
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