Information Technology Reference
In-Depth Information
. 6
. 3
Look that N 1 (
.
) =
,
N 1 (
.
) =
,
N 1 (
.
) =
.
,
N 1 (
.
) =
.
,
3
2
0
3
5
0
3
4
0
43
3
6
0
25
. 1, but N 0 (
N 1 (
3
.
8
) =
0
3
.
2
) =
0
.
8
,
N 0 (
3
.
5
) =
0
.
5
,
N 0 (
3
.
6
) =
0
.
4
,
N 0 (
3
.
4
) =
0
.
6
,,
N 0 (
3
.
6
) =
0
.
4
,
N 0 (
3
.
8
) =
0
.
2.
Example 2.2.52
The negation is linear, and the standard algebra must verify the
x
10
μ = μ · ˃ + μ · ˃ . Determine the triplet
law
(
T
,
S
,
N
)
, and with
μ(
x
) =
(in
X
=[
0
,
10
]
) and
1
,
if x
∈[
0
,
5
]
7
x
˃(
x
) =
,
if x
∈[
5
,
7
]
2
0
,
if x
∈[
7
,
10
]
μ · ˃ + μ · ˃ = μ
μ · ˃ + μ · ˃ = ˃
· ˃ ) = ˃ + μ
· ˃ .
check that
,
, and
Solution . From N linear, N
=
N 0 , it follows that we can take
˕ =
id, and
μ · ˃ + μ · ˃
W ˕
from
= μ
it follows T
=
prod
, S
=
, and N
=
N
. Hence
˕
˕
W ,
(
T
,
S
,
N
) = (
prod
,
N
)
.
0
x
5
μ (
x
˃ (
Since
x
) =
1
10 , and
x
) =
,itfollows
2
1
x
10
x
x
10
0
x
1
(
7
x
)
, μ˃ (
(
x
5
)
, μ ˃(
7
x
x
μ˃(
x
) =
x
) =
x
) =
(
1
10 )
.
20
20
2
x
10
0
0
Hence,
x
x
10
W (
10 ,
0
) =
x
10 = μ(
· ˃ + μ · ˃ )(
x
(
7
x
)
x
(
x
5
)
W (
x
10
x
) =
=
x
),
,
) =
20
20
W (
x
x
10
,
10 ) =
0
W (
x
x
10 ,
1
10 ) =
1
· μ + ˃ · μ )(
x
(
7
x
)
W (
7
x
x
7
x
x
) =
= ˃(
x
).
,
(
1
10 ) =
20
2
2
W (
0
,
0
) =
0
Finally, since,
 
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