Information Technology Reference
In-Depth Information
~
using gravity method (1.8).
It is resulted in definite numbers which will be denoted with
~
X
, and
Let us defuzzificate fuzzy numbers
,
m
1
A
,
n
=
1
N
,
B
,
B
, accordingly.
Number
m
A
,
n
=
1
N
is referred to as point
-wis
e rating of manifestation of
qualitative characteristic
X
for
n
-th object,
.
n
=
1
N
Let us compute normalized rating by the formula
A
−
B
E
=
n
1
B
.
(5.8)
n
B
−
m
1
Evaluation
E
is referred to as a degree of characteristic
X
manifestation
intensity for
n
-th object.
E
range is a segment [0.1].
Thus, the method allows quantitative evaluations of qualitative characteristics'
manifestations.
If it is
ne
cessary to assign one of qualification levels (one of linguistic values
X
,
of characteristic
X
) to
n
-th object, we can use the following
indexes, without limiting a generality,
l
=
1
m
1
[
]
() ()
∫
min
η
x
,
μ
x
dx
n
l
l
n
λ
=
∫
0
,
l
=
1
m
,
n
=
1
N
(5.9)
1
[
() ()
]
max
η
x
,
μ
x
dx
n
l
0
or
1
()
()
l
n
∫
σ
=
η
x
−
μ
x
dx
,
l
=
1
m
,
n
=
1
N
.
(5.10)
n
l
0
(
)
~
~
j
n
l
n
j
n
l
n
If
λ
=
max
λ
σ
=
max
σ
, the possibility of equality
and
—
j
~
~
(
)
Pos
A
=
X
is calculated. According to [153]
n
j
~
~
[
]
(
)
() ()
Pos
A
=
X
=
max
min
η
x
,
μ
x
.
n
j
n
j
x
~
~
(
)
is assigned to
n
-th object with the
If
Pos
A
=
X
=
γ
, then qualification level
X
n
j
j
possibility
.
γ
5.2 Determinatio n of O bject Ratings a nd Q ualification Levels
5.2 Determination of Object Ratings and Qualification Levels
by Several Qualitative Characteristics Measured in Marks
and Verbal Scales
5.2 Determinatio n of O bject Ratings a nd Q ualification Levels
Let us consider a group of objects which are estimated by several qualitative char-
acteristics. To measure these characteristics ordinal scales are used. With
mark evaluations assigned to objects of the group, problem to aggregate these
