Information Technology Reference
In-Depth Information
k
[
]
⎛
[
]
⎞
()
()
()
()
()
()
∑
min
μ
x
,
μ
x
,...,
μ
x
=
ω
min
μ
x
,
μ
x
,...,
μ
x
≤
⎜
⎝
⎟
⎠
1
l
2
l
kl
i
1
l
2
l
kl
i
=
1
k
i
=
1
k
i
=
1
k
k
⎛
⎞
()
()
[
()
()
()
]
∑
∑
≤
f
x
=
ω
μ
x
≤
ω
max
μ
x
,
μ
x
,...,
μ
x
=
⎜
⎝
⎟
⎠
l
i
il
i
il
2
l
kl
i
=
1
k
i
=
1
i
=
1
[
()
()
()
]
[
]
=
max
μ
x
,
μ
x
,...,
μ
x
;
∀
x
∈
0
,
l
=
1
m
,
1
l
2
l
kl
i
=
1
k
(4.6)
then from (4.6) it is obtained
[
]
()
()
()
()
≤
min
μ
x
,
μ
x
,...,
μ
x
≤
f
x
1
l
2
l
kl
l
i
=
1
k
[
()
()
()
]
[
]
μμ
Thus, the generalized model of expert qualitative characteristic evaluations or
expert description, in linguistic terms, of physical values of the quantitative
characteristic constructed in §4.1 with use of the least squares method, is Pareto
optimal one.
4
.2 Definit ion of Weig ht Coefficients of the For mal ize d Result
s
≤
max
x
,
x
,...,
μ
x
;
∀
x
∈
0
,
l
=
1
m
.
1
l
2
l
kl
i
=
1
k
4.2 Definition of Weight Coefficients of the Formalized Results
of Expert Qualitative Characteristic Evaluations Based on
the Similarity Relations
[
]
4
.2 Definit ion of Weig ht Coefficients of the For mal ize d Result
s
Let similarity relations with matrixes
(
)
R
= μ
X
,
X
,
i
=
1
k
,
j
=
1
k
;
1
R
i
j
1
[
]
(
)
R
= μ
M
,
M
,
i
=
1
k
,
j
=
1
k
, accordingly, and conformity relations with
1
R
i
j
1
(
)
(
)
ˆ
ˆ
matrixes
;
, accordingly, are constructed based
=
μ
X
,
X
=
μ
M
,
M
1
R
i
j
1
R
i
j
1
1
on sets
k
and
using similarity indexes.
Ξ
k
Θ
[
]
[
]
(
)
(
)
R
=
μ
M
,
M
Let similarity relations with matrixes
R
=
μ
X
,
X
;
,
2
R
i
j
2
R
i
j
2
2
(
)
ˆ
accordingly,
and
conformity
relation
with
matrix
=
μ
X
,
X
;
2
R
i
j
2
(
)
ˆ
=
μ
M
,
M
are constructed based on sets
k
and
Θ
k
using consistency
Ξ
2
R
i
j
2
ˆ
indexes. According to the decomposition theorem, the matrix
,
can de
p
=
1
2
p
decomposed onto equivalence relations
⎧
1
.
.
.
⎫
⎛
δ
δ
⎞
12
1
k
⎜
⎟
⎟
⎪
⎪
⎨
⎪
⎪
⎬
δ
1
.
.
.
δ
⎜
⎜
ˆ
12
2
k
=
max
α
,
p
=
1
2
⎟
p
.
.
.
.
.
.
α
⎪
⎩
⎪
⎭
⎜
⎜
⎟
⎟
⎪
⎪
δ
δ
.
.
.
1
⎝
⎠
1
k
2
k
0
⎩
⎨
⎧
δ
=
i
=
1
k
,
j
=
1
k
.
where
ij
1
