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evaluations in a certain uniform index arises rather often. This index is a final
rating index of object within the limits of considered characteristics and is used,
for example, to assign the object with qualification level available among the ac-
cepted ones [23, 25, 174—179]. Building of final ratings based on arithmetical
operations is incorrect because of incomparability, in sense and content, of object
evaluations within the limits of different qualitative characteristics.
Therefore, we offer to construct convolution of comparable abstract values of
indexes membership to COSS terms as the final rating. Transformation of evalua-
tions of characteristic manifestation to values of COSS membership functions
corresponds to measurement of these characteristics within a uniform scale and
ensures adequacy of model below for determination of the general ratings of units
within the limits of several characteristics.
Y
The ch aracteristics measured in mark scales. Let qualitative characteristics
,
j
j 1= be estimated for the gro up o f N o bje cts. To estimate these characteristics
mark scales with elements
k
j
=
1
k
y
=
0
K
,
, acc ordingly, are used. Let us intro-
j
j
0
s
1
duce normalized marks
s
=
y
/
K
,
y
=
0
K
,
. Thus,
,
j
=
1
k
j
j
j
j
j
j
j
=
1
k
. Following the evaluation results of all charac teri stics, it is necessary to
assign one of the accepted qualification levels
to the objects. Levels
are arranged in ascending order of characteristic manifestation intensity degree.
Let us construct COSS with terms
X ,
l
=
1
m
X ,
using the method described in
§2.2. Relative contents of objects (probably, of certain ideal group) a priori set
within the limits of each qualification level are taken as parameters necessary for
model-building of COSS. For example, if qualification levels are assigned to the
enterprise employees, necessary parameters for building of COSS can be defined
on the basis of the selected vacancy jobs within the limits of each qualification
level.
Let us denote membership functions of fuzzy numbers
l
=
1
m
~
corresponding to
l
() (
)
l
l
l
L
l
R
μ
x
a
,
a
,
a
,
a
terms
X with
. Let for n -th object,
n
=
1
N
, manifesta-
l
1
2
y ,
n
tions of characteristics Y ,
j
=
1
k
j
=
1
k
are estimated by numbers
,
()
n
j
s
n
j
μ
l s
n
=
1
N
, or normalized numbers
,
j
=
1
k
,
n
=
1
N
, accordingly. Then
,
j
=
1
k
,
n
=
1
N
are membership degrees of normalized marks to fuzzy numbers
~
= .
Let us introduce the
l
1
m
,
l
M matrix,
, with columns being degrees of
n
=
1
N
n
s ,
of n -th object
membership of normalized marks
j
=
1
k
n
=
1
N
to fuzzy
~
l
=
1
m
numbers
,
:
l
 
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