Information Technology Reference
In-Depth Information
l
k
()
()
∑
∑
ωλ
(5.32)
Let us compute the sum of these
coef
ficient
s, usin
g cha
rac
teristics of COSS and
definition of functions
n
i
=
μ
x
n
j
+
ω
δ
x
n
v
,
i
=
1
n
=
1
N
.
j
ij
v
i
j
=
1
v
=
l
+
1
()
n
v
n
=
1
N
v
=
l
+
1
k
i
=
1
δ
i
x
,
,
,
.
5
[
()
()
()
]
∑
=
n
i
n
n
n
λ
=
ω
μ
x
+
μ
x
+
...
+
μ
x
+
...
1
11
1
21
1
51
1
i
1
()
()
()
[
]
+
+
ω
μ
x
n
l
+
μ
x
n
l
+
...
+
μ
x
n
l
l
1
l
2
l
5
l
(
)
(
)
(
)
[
]
n
l
n
l
n
l
+
ω
δ
x
+
δ
x
+
...
+
δ
x
+
...
l
+
1
1
+
1
2
+
1
5
+
1
[
() ()
()
]
5
∑
=
n
k
n
k
n
k
+
ω
δ
x
+
δ
x
+
...
+
δ
x
=
ω
=
1
.
k
1
2
5
j
i
1
n
i
λ
Based on the above, we may consider coefficients
,
,
as weight
i
=
1
n
=
1
N
coefficients of terms of characteristic
Y
for
n
-th object,
n
=
1
N
. A fuzzy rating
of
n
-th object within the limits of characteristics
X
,
is determined as
j
=
1
k
j
fuzzy number
~
~
~
n
n
A
=
λ
⊗
Y
⊕
...
⊕
λ
⊗
Y
n
1
1
5
5
(5.33)
with membership function
⎛
5
5
5
5
⎞
()
∑
∑
∑
∑
n
i
n
i
n
i
n
i
μ
x
≡
⎜
⎝
λ
a
,
λ
a
,
λ
a
,
λ
a
⎟
⎠
,
n
i
1
j
2
jL
iR
i
=
1
i
=
1
i
=
1
i
=
1
~
(
)
Y
≡
a
,
a
,
a
,
a
.
where
i
i
1
i
2
iL
iR
y
. If confidence
Let us define a confidential interval for obtaining definite rating
()
α
y
of
n
-th object lies within the interval
level is
μ
n
y
≥
,
0
< α
<
1
, rating
n
5
5
5
5
(
)
(
)
∑
∑
∑
∑
λ
n
i
a
−
1
−
α
λ
n
i
a
≤
y
≤
λ
n
i
a
+
1
−
α
λ
n
i
a
.
j
1
jL
n
j
2
jR
i
=
1
i
=
1
i
=
1
i
=
1
~
Let us defuzzificate fuzzy number
using the gravity method; let us denote the
obtained definite number with
A
.
To recognize success of objects' functioning it is necessary to identify fuzzy
number having membership function
()
μ
x
with one of COSS terms named
Y
n
~
,
()
μ
x
(with one of fuzzy numbers
i
=
1
with membership functions
,
i
). For this purpose let us calculate identification indexes:
i
=
1
