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~
~
(
)
D is assigned to n -th object with a
If
, qualification level
Pos
A
=
D
=
γ
n
j
possibility γ
.
5.3 O btai ni ng of Rati ng Po ints of G roups of Objects
5.3 Obtaining of Rating Points of Groups of Objects within the
Scope of a Qualitative Characteristic
5.3 O btai ni ng of Rati ng Po ints of G roups of Objects
In §5.1—5.2 methods used to obtain rating points of objects within the limits of
one and several qualitative characteristics are described. However in practice there
are problems of obtaining rating points within the limits of one and several
qualitative characteristics for both individual objects, and groups of objects.
Let us consider k groups of objects, for which intensity of manifestation of
qualitative characteristic X is estimated within the limits of a verbal scale with
levels
X . Let us denote a relative amount of objects of j -th group referred to
a
j
X , with
level
, and a relative amount of units of all groups referred to level
l
X ,
l
=
1
m
a .
, with
a , let us construct COSS X with terms
Based on
X ,
l
=
1
m
and member-
~ . Let us
define a fuzzy rating of j -th group of objects within the limits of manifestation of
qualitative characteristic X in the form of fuzzy number
() (
)
l
l
l
L
l
R
ship functions
μ
x
b
, 2
b
,
b
,
b
of corresponding fuzzy numbers
l
1
l
~
with membership
j
function
j
j
j
m
β
=
a
μ
a
μ
...
a
μ
,
(5.25)
j
1
1
2
2
m
or
m
m
m
m
β
a
j
b
l
,
a
j
b
l
,
a
j
b
l
L
,
a
j
b
l
R
.
(5.26)
j
l
1
l
2
l
l
l
=
1
l
=
1
l
=
1
l
=
1
Let us define a confidential interval for definite rating z , characterizing manifes-
tation of characteristic X for j -th group of objects. With confidence level
( )
, rating z of characteristic X manifestation for j -th
group of objects lies within the interval
β
j z
α
,
0
< α
<
1
j
m
m
m
m
()
()
j
l
1
j
l
L
j
l
1
j
l
R
a
b
L
α
a
b
z
a
b
+
R
α
a
b
.
l
1
l
j
l
2
l
l
=
1
l
=
1
l
=
1
l
=
1
β
j
=
1
k
μ
Let us defuzzificate fuzzy numbers with membership functions
,
,
,
j
1
μ
C ,
B ,
B . Let us refer
. Let us denote the obtained numbers with
j
=
1
k
,
m
 
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