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z characterizing
Let us define a confidential interval for obtaining rating
for i -th group of objects.
X ,...,
1
X
manifestation of qualitative characteristics
m
(
)
() α
i
i
i
i
R
Let
λ
Δ
,
Δ
,
Δ
,
Δ
, then with confidence level
λ
i z
,
rating
0
< α
<
1
i
1
2
L
i
z of manifestation of characteristics
X ,...,
1
X
for i -th groups of objects lies in
m
an interval
()
()
(5.30)
i
1
i
i
1
i
Δ
L
α
Δ
z
Δ
+
R
α
Δ
.
1
L
i
2
R
Let us defuzzificate fuzzy numbers with membership functions
η
ω
μ
1
1
...
ω
μ
p
;
λ
,
i
=
1
k
;
=
i
1
m
1
1
p
k
δ
=
ω
μ
...
ω
μ
.
1
k
m
1
p
, B , C . Number A is
referred to as a pointwise rating of manifestation of qualitative characteristics
A ,
Let us denote the obtained fuzzy numbers with
i
=
1
k
X ,...,
1
X
.
Let us compute normalized rating for i -th group of objects by the formula
for i -th group of objects,
i
=
1
k
m
= (5.31)
The evaluation E is referred to as an average intensity degree of manifestation of
qualitative characteristics
A
B
E
i
.
i
C
B
for i -th group of objects. Range of
E ,
X ,...,
1
X
m
is a segment [0, 1].
It is worth mentioning that to operate with various qualitative characteristics,
authors use abstract concepts — membership functions of linguistic values of
these characteristics. As known, operations for linguistic values are defined on the
basis of triangular norms and triangular conorms, and therefore, they are not
familiar arithmetical operations.
5.5 O btai ni ng of Rati ng Po ints of O bjects
i
=
1
k
5.5 Obtaining of Rating Points of Objects within the Limits of
Several Quantitative and Qualitative Characteristics
5.5 O btai ni ng of Rati ng Po ints of O bjects
Let us con sider a group of N objects, for which quantitative characteristics
l
X j
,
j
=
1
,
and intensities of manifestation of qualitative characteristics
X ,
are estimated. In aggregate, estimated characteristics make essential
influence on characteristic Y , for example, success of functioning of objects, be-
ing estimated within the limits of the scale: Y = “extremely unsuccessful”,
v
=
l
+
1
k
Y =
Y = “mean successful",
“unsuccessful”,
Y = "rather successful",
Y =
"extremely successful".
 
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