Information Technology Reference
In-Depth Information
(
)
n
~
(
)
∑
=
ˆ
k
k
L
k
R
2
F
b
,
b
,
b
=
f
Y
,
Y
,
i
i
which characterizes an affinity measure between initial and model output data:
i
1
⎧
2
n
1
(
)
⎪
⎨
⎡
(
)
⎤
∑
=
k
k
L
k
R
1
k
k
L
k
R
i
i
L
F
b
,
b
,
b
=
θ
b
,
b
,
b
−
y
+
y
+
⎢
⎣
⎥
⎦
Y
1
6
⎪
⎩
i
i
1
2
⎫
1
⎡
(
)
⎤
⎪
⎬
2
k
k
L
k
R
i
i
R
+
θ
b
,
b
,
b
−
y
−
y
.
⎢
⎣
⎥
⎦
2
Y
6
⎪
⎭
i
The optimization problem is set as follows:
n
(
)
(
)
~
∑
=
k
k
L
k
R
2
F
b
,
b
,
b
=
f
Y
,
Y
→
min,
i
i
i
1
(
)
.
m
m
+
3
b
k
L
≥
0
b
k
R
≥
0
k
=
0
2
(
)
(
)
1
k
k
L
k
R
2
k
k
L
k
R
θ
b
,
b
,
b
θ
b
,
b
,
b
Since
and
are piecewise linear functions in the field
Y
Y
i
i
(
)
,
m
m
+
3
k
L
k
R
b
≥
0
b
≥
0
k
=
0
2
then
F
is piecewise differentiable function, and solutions of an optimization
problem are determined by means of known methods [15
2].
Let initial output data
~
(
)
i
i
i
L
i
R
,
i
=
1
n
are formalizations
Y
≡
y
,
y
,
y
,
y
1
2
~
(
)
k
k
k
L
k
R
Y
of an attribute
Y
. In the
Y
≡
y
,
y
,
y
,
y
,
k
=
1
p
of linguist
ic
values
1
2
determining model output data
a problem of predicting linguistic
values of this attribute or identification of each fuzzy numbers
Y
,
i
=
1
n
with one of
Y
i
~
arises.
fuzzy numbers
[
]
i
i
Let us denote with
A
1
,
A
,
i
=
1
n
the weighed segments of output model data
2
[
]
Y
k
k
,
i
=
1
n
, and with
B
1
,
B
,
k
=
1
p
- the weighed segments of formalizations
2
~
(
)
k
k
k
L
k
R
Y
≡
y
,
y
,
y
,
y
Y
,
,
k
=
1
p
of linguistic values
k
=
1
p
of attribute
Y
.
k
1
2
Then
~
(
)
(
)
(
)
2
2
2
i
k
i
k
f
Y
,
Y
=
A
−
B
+
A
−
B
;
i
=
1
n
;
k
=
1
p
.
i
k
1
1
2
2
Y
Output model value
is identified with linguistic value
Y
, if
~
~
(
)
(
)
2
2
f
Y
,
Y
=
min
f
Y
,
Y
;
k
=
1
p
.
i
s
i
k
k
