Information Technology Reference
In-Depth Information
Let us defuzzificate fuzzy numbers
X and
~
~ using gravity
method (1.8). As a result, we obtain definite numbers to be denoted with
,
n
=
1
N
,
1
m
~
,
n
=
, B , B , accordingly.
The number
1
N
A ,
is referred to as a pointwise rating of manifestation of
n
=
1
N
characteristic Y ,
for n -th object.
Let us compute normalized rating by the formula
j
=
1
k
A
B
(5.16)
E
=
n
1
,
n
=
1
N
.
n
B
B
m
1
n
=
1
N
Let the evaluation
E ,
be referred to as average intensity degree of
for n -th object,
manifestation of characteristics
Y ,
n
=
1
N
. Range of
j
=
1
k
E ,
n
=
1
N
is a segment [0, 1]. Thus, the method allows to obtain quantitative
evaluations of manifestations of several qualitat ive characteristics.
To assign one of qualification levels
X ,
to n -th object, it is necessary
l
=
1
m
~
v ,
to identify fuzzy number
,
n
=
1
N
having membership function
n
=
1
N
~
()
μ
x
wit h on e of fuzzy numbers
,
l
=
1
m
with membership functions
,
l
l
l
=
1
m
. For this purpose, let us calculate identification indexes:
1
[
() ()
]
min
μ
x
,
v
x
dx
l
n
λ
l
n
=
0
,
l
=
1
m
,
n
=
1
N
(5.17)
1
[
() ()
]
max
μ
x
,
v
x
dx
l
n
0
or
1
()
()
(5.18)
l
n
σ
=
v
x
μ
x
dx
,
l
=
1
m
,
n
=
1
N
.
n
l
0
If
(
)
j
n
l
n
j
n
l
n
λ
=
max
λ
,
σ
=
max
σ
,
l
l
~
~
(
)
then
is calculated.
Pos
A
=
X
n
j
~
~
(
)
If
, then qualification level
is assigned to n -th object with
X
Pos
A
=
X
=
γ
n
j
j
the possibility
.
The described method of obtaining object ratings within the scope of several
qualitative characteristics is applicable under condition of measurement of all in-
dications in ordinal numerical scales. The example illustrating the described
method is followed with the method of obtaining object ratings within the scope of
the several qualitative characteristics measured in verbal scales.
γ
 
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