Information Technology Reference
In-Depth Information
g
more information is needed, but in the absence of it, we
can decide to take the linear models
f
To determine
f
and
x
−
32
5
43
−
x
(
)
=
g(
)
=
x
, and
x
, with which
2
3
5
,
1
2
.
μ
A
g
e
(
p
)
(
)
=
μ
A
g
e
(
p
)
(
)
=
35
42
As it will be seen later on, 0.6 is the
possibility
that
A
g
e
(
p
)
=
35, and 0.5 that
of
A
g
e
(
p
)
=
42. Hence, it seems a little bit more possible that it be '
A
g
e
(
p
)
=
42'
than '
A
g
e
(
p
)
=
35'.
Example 2.2.49
Knowing that Height(John)
=
175 cm, and Height(Peter)
=
180 cm,
consider the two statements:
p
=
It is false that John is not very tall or is more or less short
q
=
It is false that Peter is not very tall or is more or less short.
which is more true?
Solution
. Both statements can be written by
Is false that
x
is
P
,
with
P
=
'(not very tall) or (more or less short)'.
Hence
(μ
v
er y t all
(
2
μ
P
(
x
)
=
S
x
), μ
not short
(
x
))
=
S
(
N
(μ
tall
(
x
)
),
μ
tall
(
A
(
x
)) ),
with a continuous t-conorm
S
, a strong negation
N
,andasymmetry
A
on
X
, provided
x
varies in a scale of heights.
What should be compared are the two values
N
(μ
P
(
))
(μ
P
(
))
175
and
N
180
, and
μ
tall
. Let us take
for that it is needed to know
⊧
⊨
0
,
if
x
∈[
0
,
150
]
μ
tall
(
x
)
=
strictly non decreasing
,
if
x
∈[
150
,
190
]
⊩
1
,
if
x
∈[
190
,
210
]
with, perhaps,
μ
tall
(
x
)
=
0
.
025
x
−
3
.
75
,
x
∈[
150
,
190
]
, if we need to have numbers.
Hence, with
A
(
x
)
=
210
−
x
,
it is
A
(
175
)
=
210
−
175
=
35
,
and
μ
tall
(
35
)
=
0,
as well as
A
(
180
)
=
220
−
180
=
30, and
μ
tall
(
30
)
=
0, because of that
2
μ
P
(
175
)
=
S
(
N
(μ
tall
(
175
)),
0
)
=
N
(μ
tall
(
175
)
)
2
μ
P
(
180
)
=
S
(
N
(μ
tall
(
180
)),
0
)
=
N
(μ
tall
(
180
)
)
.
Since
μ
tall
is strictly non-decreasing between 150 and 190, it is
μ
tall
(
175
)<
2
2
μ
tall
(
180
)
, and
N
(μ
tall
(
180
)
)<
N
(μ
tall
(
175
)
)
. Finally,
2
2
2
2
N
(
N
(μ
tall
(
175
)
)) <
N
(
N
(μ
tall
(
180
)
))
,or
μ
tall
(
175
)
< μ
tall
(
180
)
,
and
q
is strictly more true than
p
.
Search WWH ::
Custom Search