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In this paragraph we offer to construct convolution of comparable components
of a membership of these evaluations to the fuzzy numbers which formalize lin-
guistic values of estimated qualitative characteristic instead of convolution of the
intermediate evaluations obtained.
Let us consider a group
N
of objects which are estimated within the limits of
manifestation of a qualitative characteristic
X
. Rating points are defined on the
basis of mark evaluations
k
for sub-characteristics, which compose the character-
istic. A minimum quantity of points with which an object can be estimated within
the scope of
i
-th sub-ch
arac
teristic is equal to zero, and a maximum quantity of
points is equal to
.
Let us denote a
n e
valuation of
n
-th object
Z
,
i
=
1
k
in the scope of
i
-th sub-
n
=
1
N
i
=
1
k
n
i
z
. Let us normalize evaluations
n
i
z
,
characteristic
with
and
i
=
1
k
present result of the evaluation of
n
-th object in the form of the vector
⎛
n
n
z
n
k
⎞
z
z
(
)
n
n
n
k
⎜
⎜
⎝
1
,
2
,...,
⎟
⎟
⎠
=
m
,
m
,...,
m
,
n
=
1
N
.
(5.1)
1
2
Z
Z
Z
1
2
k
l
=
1
m
Let
be levels of a verbal scale arranged by increase of intensity of
characteristic
X
and applied to the estimate purpose. Within the limits of the
building m
eth
od (see § 2.2) of
C
OSS with title
X
and membership functions
()
X
,
μ
x
,
l
=
1
m
of terms
X
,
l
=
1
m
is carried out. The fuzzy numbers correspond-
l
~
. The amount of terms is defined by an
amount of accepted (or specially developed) verbal levels of intensity of charac-
teristic manifestations
X
. According to the requirements to membership functions
of COSS terms, for vector co-ordinates (5.1) validity of the following equalities
follows:
X
are denoted with
ing to terms
l
⎛
m
⎞
m
()
()
∑
∑
n
i
n
i
n
i
n
i
n
i
m
=
m
⋅
⎜
⎝
μ
m
⎟
⎠
=
m
μ
m
,
i
=
1
k
.
(5.2)
l
l
l
=
1
l
=
1
Considering a fuzziness attributed to evaluation procedure, let us in (5.2) substi-
tute normalized
eval
uations
()
n
m
in each product
m
n
i
μ
m
n
i
,
with fuzzy
l
=
1
m
l
~
numbers
, accordingly. Such procedure is referred to as fuzzifyin
g o
f
definite data [53J. Then, vector co-ordinates of evaluations of
n
-th object,
,
l
=
1
m
l
n
=
1
N
are fuzzy numbers
~
~
()
()
~
n
i
n
i
n
i
(5.3)
Parameters of these numbers are defined by component-w
ise
multiplication of pa-
rameters of
fu
zzy numbers
m
=
μ
m
⊗
X
⊕
...
⊕
μ
m
⊗
X
,
i
=
1
k
.
1
1
m
m
~
(
)
l
l
l
L
l
R
l
≡
a
,
a
,
a
,
a
,
,
l
=
1
m
by usual numbers
1
2
l
()
μ
l
m
n
i
l
=
1
m
i
=
1
k
,
,
,
n
=
1
N
and their subsequent addition, i.e. for (5.3) we
obtain
