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outcome of th
e ex
pert evaluation of qualitative chara
cteri
stic of
N
objects group
{
()
(
}
)
n
n
n
n
L
n
R
n
μ
x
=
a
,
a
,
a
,
a
on the basis of the
formalized results
M
of an evaluation made by
k
experts of an object group
within the scope of a qualitative characteristic.
Let us formulate Pareto condition for the optimum generalized result of
M
expert evaluation of qualitati
ve c
haracteristic of an object group constructed on
the basis of elements
M
= μ
,
n
=
1
N
,
,
n
=
1
N
1
2
M
,
i
=
1
k
k
of the set
Θ
:
k
k
∩
M
⊆
M
⊆
∪
M
i
i
i
=
1
i
=
1
or
[
]
()
()
()
()
≤
n
n
n
k
n
min
μ
x
,
μ
x
,...,
μ
x
≤
μ
x
1
2
i
=
1
k
[
]
()
()
()
[]
(4.26)
n
n
n
k
≤
max
μ
x
,
μ
x
,...,
μ
x
,
∀
x
∈
0
,
n
=
1
N
.
1
2
i
=
1
k
Let us assume that membership functions of the generalized formalized result of
an
expert
eval
uation
of
qualitative
characteristic
of
units
group
{
}
M
=
μ
n
,
n
=
1
N
belong to the same class of functions as membership
n
i
μ
Θ
k
functions of set
elements, i.e. if
are membershi
p fun
ctions of tolerance or
μ
n
n
=
N
unimodal numbers from an
are also defined as
membership functions of tolerance or unimodal numbers from the
group, then
,
1
Λ
gro
up.
Λ
ω
Let within the limits of a method 4.3 weight coefficients
,
of the set
i
=
1
k
i
n
n
n
L
n
R
of
membership functions of the generalized formalized outcome of an expert
evaluation of qualitative characteristic of an object group from the condition
Θ
k
elements are defined. We determine parameters
a
,
a
,
a
,
a
,
i
=
1
N
1
2
[
]
N
k
(
)
(
)
(
)
(
)
∑∑
==
2
2
2
2
in
n
in
n
in
L
n
L
in
R
n
R
Ф
=
ω
a
−
a
+
a
−
a
+
a
−
a
+
a
−
a
→
min
.
i
1
1
2
2
(4.27)
n
11
i
Parameters are determined from the system of normal equations with
:
n
=
1
N
k
∂
F
⎡
k
⎤
∂
F
⎡
⎤
∑
=
∑
=
in
n
=
2
ω
a
in
−
a
n
=
0
=
2
ω
a
−
a
=
0
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
i
1
1
i
2
2
∂
a
n
∂
a
n
i
1
i
1
1
2
∂
F
⎡
k
⎤
∂
F
⎡
k
⎤
∑
=
in
L
n
L
∑
=
=
2
ω
a
−
a
=
0
in
R
n
R
=
2
ω
a
−
a
=
0
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
i
(4.28)
n
L
i
∂
a
n
R
∂
a
i
1
i
1
We obtain the solutions:
k
k
k
k
1
∑
=
∑
=
2
∑
=
∑
=
n
R
in
R
a
n
=
ω
a
in
;
n
L
in
L
a
=
ω
a
.
a
n
=
ω
a
in
;
a
=
ω
a
;
(4.29)
i
1
2
i
i
i
i
1
i
1
i
1
i
1
