Information Technology Reference
In-Depth Information
(
)
ji
j
ji
j
ji
j
L
ji
L
j
ji
L
j
L
ji
j
R
ji
R
j
ji
R
j
R
x
b
,
x
b
,
x
b
+
x
b
−
x
b
,
x
b
+
x
b
+
x
b
,
j
=
1
m
,
i
=
1
n
.
Using the proposition 6.1, let us compute the weighed segments
[
1
2
1
2
]
~
. Let us denote weighed segments
y
i
−
ly
i
L
,
for observable output data
y
i
+
ry
i
R
1
2
~
~
i
j
of products of numbers
and
with
j
[
]
(
)
(
)
1
j
j
L
j
R
2
j
j
L
j
R
θθ
(6.7)
According to the proposition 6.3, boundaries of segments (6.7) are stipulated by
linear combinations of products of parameters of fuzzy numbers
b
,
b
,
b
,
b
,
b
,
b
,
j
=
1
m
,
i
=
1
n
~
~
~
~
i
i
j
a
X
a
X
j
j
j
~
~
i
j
and
,
j
~
(
)
X
i
j
≡
x
ji
,
x
ji
,
x
ji
L
,
x
ji
R
j
=
1
m
,
i
=
1
n
. If, for example,
is positive fuzzy number,
1
2
(
)
~
(
)
a
≡
b
j
,
b
j
L
,
b
j
R
ji
ji
L
j
j
R
and
is negative fuzzy number
x
−
x
>
0
b
+
b
<
0
, then
j
1
(
)
(
)
(
)
θ
1
b
j
,
b
j
L
,
b
j
R
=
b
j
x
ji
+
rx
ji
R
−
b
j
L
lx
ji
+
mx
ji
R
;
~
~
i
j
2
2
a
X
j
(
)
(
)
(
)
2
j
j
L
j
R
j
ji
ji
L
j
R
ji
ji
L
θ
b
,
b
,
b
=
b
x
−
lx
+
b
rx
−
mx
;
~
~
1
1
i
j
a
X
j
1
1
1
()
()
() ()
∫
−
∫
−
∫
−
−
l
=
L
1
α
α
d
α
,
r
=
R
1
α
α
d
α
;
m
=
L
1
α
R
1
α
α
d
α
.
0
0
0
~
~
i
j
a
j
X
Boundaries of the weighed segments of products
for other relations
~
~
i
j
between
and
will be linear functions, too, from unknown parameters
j
b
,, (in the considered area of their values), but differing from the example
given above by coefficients of the parameters considered.
Using propositions 2.1, 2.2, 6.1 — 6.3, let us compute the weighed segments
j
j
L
b
j
R
⎡
⎤
m
m
(
)
(
)
∑
∑
0
0
1
j
j
L
j
R
0
0
2
j
j
L
j
R
b
−
lb
+
θ
b
,
b
,
b
,
b
+
rb
+
θ
b
,
b
,
b
,
i
=
1
n
⎢
⎣
⎥
⎦
~
~
~
~
L
j
R
j
a
X
a
X
j
j
j
=
1
j
=
1
~
~
~
~
~
i
i
m
For model output data
Y
=
a
+
a
X
+
...
+
a
X
.
1
0
1
1
m
Let us consider a functional
n
(
~
)
∑
=
2
F
=
f
Y
i
Y
,
,
i
which characterizes an affinity measure between initial and model output data. It
is easy to demonstrate, that
i
1
2
⎡
⎤
n
m
(
)
∑
∑
0
0
i
i
L
1
j
j
L
j
R
F
=
b
−
lb
−
y
+
ly
+
θ
b
,
b
,
b
+
⎢
⎣
⎥
⎦
~
~
L
1
i
j
a
X
j
i
=
1
j
=
1
