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50
giving
y
0
=
−
(
−
x
0
)
=
−
(
−
x
0
)
2
, that gives real
50
100
1
,or
y
0
100
1
2
2
,orto
−
(
−
x
0
)
/
(
−
x
0
)
values provi
ded
50
100
1
0, equivalent to 1
2
1
−
√
1
2
x
0
1
/
2. Since, 1
/
2
x
,itis
(
1
−
x
)
1
/
4
1
/
2. Then,
50
2
CRI
(
x
)
=
−
100
(
1
−
x
)
,
if 1
/
2
x
.
For example,
CRI
)
=
√
41
)
=
√
46
)
=
√
49
(
0
.
7
=
6
.
4,
CRI
(
0
.
8
=
6
.
78,
CRI
(
0
.
9
=
7.
3. Finally, with defuzzification by the centre of area, is:
50
(
1
−
2
x
2
),
if
x
1
/
2
50
CRI
(
x
)
=
2
(
1
−
2
(
1
−
x
)
),
if
x
1
/
2
.
50
√
50,
CRI
√
25
5
2
Notice that
CR
I
(
0
)
=
(
0
.
5
)
=
(
1
−
20
.
)
=
=
5, and
√
50.
The graphic of CRI is
CRI
(
1
)
=
3.6 Rules and Conjectures
As it was said before, the output is a logical consequence of the premises given by
the input and the rule. Notwithstanding, the situation is different if, taking the rule as
defining the system, only the input is considered as a premise. But, before to consider
this question, let us consider what happens when there is more than a single rule.
1. If
μ
Q
1
,μ
Q
2
∈
Cons
(
{
μ
P
∗
}
)
, from
μ
P
∗
max
(μ
Q
1
,μ
Q
2
)
=
μ
Q
∗
, follows
μ
Q
∗
∈
Cons
(
{
μ
P
∗
}
)
.
2. If
μ
Q
1
or
μ
Q
2
is a conjecture of
{
μ
P
∗
}
, then
μ
Q
∗
∈
Conj
(
{
μ
P
∗
}
)
. The proof
μ
Q
1
∈
(
{
μ
P
∗
}
)
follows in this way, provided it is, for instance,
Conj
,
⃒
μ
Q
∗
μ
Q
1
,μ
Q
∗
•
μ
Q
∗
=
max
(μ
Q
1
,μ
Q
2
)
⃒
μ
Q
1
μ
Q
∗
,μ
Q
2
μ
Q
∗
μ
Q
2
⃒
μ
Q
∗
(μ
Q
1
,μ
Q
2
)
min
.
μ
Q
∗
, then
μ
Q
1
, that is absurd. Hence, it is
μ
Q
∗
, and
•
If
μ
P
∗
μ
P
∗
μ
P
∗
μ
Q
∗
∈
(
{
μ
P
∗
}
)
Conj
.
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