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{
()
}
μ
x
;
l
=
1
m
. Let us consider that for
each object the expert evaluations are known, and they are levels (terms) of a
verbal scale over which the eval
uati
on is performed. Thus, if a point given by
i
-th
expert to
n
-th object
. These COSS's are elements of set
k
Ξ
il
(
)
is
l
-th level of a verbal scale, it is
unambiguously mapped on membership function
n
=
1
N
()
μ
of
l
-th COSS term. Let
us denote a point given by
i
-th expert to
n
-th representative of a population
()
x
il
()
μ
n
i
x
=
μ
x
, and a collection of the formalized evaluations given by
i
-th
il
expert
{
}
()
(
)
()
()
()
1
2
N
i
n
i
in
in
in
L
in
R
M
=
μ
x
,
μ
x
,...,
μ
x
;
μ
x
≡
a
,
a
,
a
,
a
,
i
i
i
1
2
()
()
μ
n
i
x
is one of membership functions of
i
-th element
X
=
μ
x
where
i
il
of set
.
Let us introduce some legends for operations with elements
k
Ξ
, for
which a collection
N
of fuzzy numbers with membership functions is obtained:
with cross-section of two elements
M
of set
k
Θ
M
∩
M
i
j
{
}
{
[
]
}
()
()
()
μ
n
x
=
min
μ
n
i
x
,
μ
n
j
x
,
∀
x
;
M
∩ ...
∩
M
with cross-section of elements
1
k
{
}
{
}
[
]
()
()
()
n
n
n
k
μ
x
=
min
μ
x
,...,
μ
x
,
∀
x
;
1
i
=
1
k
with union of two elements
M
∪
M
i
j
[
]
{
}
{
}
()
()
()
n
n
i
n
j
μ
x
=
max
μ
x
,
μ
x
,
∀
x
;
M
∪...
∪
M
with union of elements
1
k
{
}
[
]
⎩
⎨
⎧
⎭
⎬
⎫
()
()
()
μ
n
x
=
max
μ
n
x
,...,
μ
n
k
x
,
∀
x
;
1
i
=
1
k
M
+
M
For generalized sum of two elements
i
j
{
()
(
)
}
n
i
in
jn
in
jn
in
L
jn
L
in
R
jn
R
μ
x
≡
a
+
a
,
a
+
a
,
a
+
a
,
a
+
a
;
1
1
2
2
M
and positive value
c
For generalized product of an element
()
(
{
)
}
n
i
in
in
in
L
in
R
μ
x
≡
ca
,
ca
,
ca
,
ca
;
1
2
