Information Technology Reference
In-Depth Information
Let
~
us
defuzzificate
fuzzy
numbers
,
,
n
=
1
N
~
~
~
B
=
ω
⊗
X
⊕
...
⊕
ω
⊗
X
B
=
ω
⊗
X
⊕
...
⊕
ω
⊗
X
,
using grav-
1
11
1
k
1
k
m
1
m
1
k
m
k
1
k
ity method (1.8), and let us denote the obtained definite numbers as
A
,
n
=
1
N
,
B
,
B
.
The number
~
is referred to as a pointwise rating of manifestation
of qualitative characteristics
X
for
n
-th object.
Let us determine normalized rating of
n
-th object by the formula
,
n
=
1
N
A
−
B
n
1
B
.
E
=
(5.22)
n
B
−
m
1
Let refer the evaluation
E
as an average intensity degree of manifestation of
characteristics
X
for
n
-th object. Range of
E
is a segment [0, 1]. Thus, the
method allows to determine quantitative evaluations of manifestations of several
qualitative characteristics.
Let us assume that, by results of an evaluation of all charac
teris
tics, it is neces-
sary to assign one of accepted qualification levels
to the objects.
Levels are arra
nge
d in ascending order of their rating. Let us construct COSS with
terms
D
,
l
=
1
m
D
,
using the method described in §2.2. relative contents of objects
(probably, of a certain ideal group) a priori set within the limits of each qualifica-
tion level are taken as parameters necessary for building of COSS's. Let us denote
membership functions of fuzzy numbers
l
=
1
m
~
D
, with
, corresponding to terms
()
η
. To assign one of qualification levels
D
to
n
-th object, it is necessary to
identify fuzzy number with membership function
x
l
()
μ
x
and with one of
n
()
η
x
term-sets having membership functions
. For this purpose let us calculate
l
identification indexes:
1
[
() ()
]
∫
min
η
x
,
μ
x
dx
l
n
(5.23)
λ
l
n
=
0
1
[
() ()
]
∫
max
η
x
,
μ
x
dx
l
n
0
or
1
()
()
l
n
∫
σ
=
η
x
−
μ
x
dx
.
(5.24)
l
n
0
If
(
)
j
n
l
n
j
n
l
n
λ
=
max
λ
,
σ
=
max
σ
,
l
l
~
~
(
)
then,
is calculated.
Pos
A
=
D
n
j
