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6.6 Buil di ng of a Reference Pattern (Image) of Objects
6.6 Building of a Reference Pattern (Image) of Objects with
Qualitative Characteristics Using Fuzzy Regression Models.
Obtaining of Rating Points of Objects Based on the
Reference Pattern
6.6 Buil di ng of a Reference Pattern (Image) of Objects
When performing comparative analysis of objects with non-numerical
characteristics essential complexity is caused by lack of a reference pattern
(image); in this connection labour-consuming procedures of comparing objects
with each other are carried out, as a rule. If there are a lot of objects, labour input
of these procedures increases manifold.
Let us consider
N
objects fo
r w
hich experts estimate appearances of
qualitative characteristics
X
,
having essential impact on some final
j
=
1
m
qualitative chara
cteri
stic
Y
.
Let
l
=
1
m
X
,
b
e le
vels of the v
erb
al scales applied to an evaluation of
lj
j
X
,
characteristics
be levels of the verbal scale applied
to an evaluation of characteristic
Y
, accordingly. Levels are arranged in ascending
order of intensity of appearances of these characteristics.
Let us denote relative
numb
ers of objects of the considered group, which are
referred to level
, and
Y
,
j
=
1
m
l
=
1
k
l
=
1
m
X
X
,
,
while estimating the characteristic
,
j
=
1
m
lj
j
j
l
=
1
m
, with
a
,
j
,
;
j
=
1
m
j
=
1
m
j
m
j
∑
=
Based on these d
ata
and the method described
in §
2.2, le
t us
construct COSS with
names
j
a
=
1
j
=
1
m
.
l
l
1
X
,
and term-sets
X
,
,
. Let us denote with
j
=
1
m
l
=
1
m
j
=
1
m
lj
~
()
μ
x
membership function of fuzzy number
corresponding to
l
-th term-set
lj
lj
~
j
-th COSS,
of
,
. Let us denote fuzzy numbers
,
,
l
=
1
m
j
=
1
m
l
=
1
m
lj
()
μ
x
l
=
1
m
or their membership functions
;
,
with object
j
=
1
m
j
=
1
m
lj
j
~
()
(
)
n
j
n
j
n
j
n
j
n
jL
n
jR
μ
x
≡
a
,
a
,
a
,
a
evaluations. Let us denote with
and
,
n
=
1
N
,
1
2
X
. Fuzzy
an evaluation of
n
-th unit within the limits of attribute
j
=
1
m
~
()
n
j
n
j
μ
x
number
with membership function
is equal to one of fuzzy numbers
~
l
=
1
m
a
,
,
,
j
=
1
m
. Let u
s d
enote with
l
=
1
k
relative numbers of the
lj
j
Y
,
objects referred to level
=
while estimating the characteristic
Y
.
Based on these data, let us construct COSS with name
Y
and term-set
l
1
k
Y
,
~
()
μ
x
l
=
1
k
. Let us denote with
membership function of fuzzy number
l
~
,
Y
,
corresponding to term
. Let us refer fuzzy numbers
or their
l
=
1
k
l
=
1
k
