Information Technology Reference
In-Depth Information
Sixth Step: Several Rules with Numerical Input
The problem is now
By using the CRI,
R
1
with the input “
x
is
P
∗
” gives an output “
y
is
Q
1
”, with
μ
Q
1
its membership function and
R
2
with the input “
x
is
P
∗
”gives“
y
is
Q
2
” with
μ
Q
2
its membership function. The total output, “
y
is
Q
∗
”, corresponds to the idea
(
y
is
Q
1
)
or
(
y
is
Q
2
), and translating this '
or
' by means of the lowest t-conorm its
value can be obtained by
.
For example, the Mandani's method consist in taking
J
μ
Q
∗
(
y
)
=
Max
(μ
Q
1
(
y
), μ
Q
2
(
y
))
(
a
,
b
)
=
Min
(
a
,
b
)
and
the Larsen's method, in taking
J
(
a
,
b
)
=
a
·
b
. Let us consider in
X
=[
0
,
10
]
,
Y
=[
0
,
1
]
the problem:
R
1
:
If
x
is
close
-
to
4
,
then
y
is
big
R
2
:
If
x
is
small
,
then
y
is
small
x
=
3
.
5
μ
Q
∗
using both methods by supposing “
close
-
to
4” as in the former
and let us find
x
10
example,
μ
big
(
y
)
=
y
,
μ
small
(
x
)
=
1
−
, and
μ
small
(
y
)
=
1
−
y
.
The outputs
Q
1
,
Q
2
are:
μ
μ
IF
THEN
close-to
4
big
1
1
μ
∗
Q
1
R1:
0.5
0
1
4
5
0
0.5
3
10
μ
IF
THEN
μ
small
small
1
1
μ
0.65
2
Q
R2:
0
1
0
0.35
3.5
10
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