Information Technology Reference
In-Depth Information
1
2
5
9
⎛
⎞
⎜
⎟
1
1
2
5
⎜
⎟
2
⎜
⎟
1
1
A
=
.
⎜
⎟
1
2
2
⎜
⎟
5
2
⎜
⎟
1
1
1
1
⎜
⎟
⎝
9
5
2
⎠
λ
=
4
008
We determine eigenvalues of this matrix:
;
λ
=
−
0
004
;
1
2
λ
=
−
0
001
+
0
175
i
;
λ
=
−
0
001
−
0
175
i
. Let us select a maximum eigenvalue
3
4
(
)
ω
=
0
879
;
0
427
;
0
191
;
0
093
and the corresponding eigenvector
. Let us build
2
xy
by four points (0.3; 0.879), (0.2; 0.427),
(0.1; 0.191), (0; 0.093), applying a method of least squares. Let us check the value
(
=
2
−
0
01
a line
)
x
=
0
0038
y
=
1
x
=
0
39
y
0
59
=
1
534
−
0
01
=
1
524
. With
y
=
0
,
; with
,
.
()
()
μ
x
μ
x
Thus, the left and right boundaries of membership functions
and
3
2
are defined. To complete constructing the functions, let us find the equation of a
line
, which is passing through two points (0.39; 1), (0.59; 0). This
line will limit membership function
y
=
2
95
−
5
x
()
μ
x
on the right, and the line
2
()
μ
x
y
=
1
−
2
95
+
5
x
=
5
x
−
1
95
will limit membership function
on the left.
3
Thus,
() (
)
() (
)
=
μ
x
0
59
;
0
2
0
385
μ
x
=
0
39
;
0
3862
;
0
2
;
.
3
2
()
()
μ
x
μ
x
Membership function
is defined using function
in the following
1
2
manner:
() (
)
μ
x
=
0
0
0038
;
0
0
3862
1
2.4 Formalization of Linguistic Values of Characteristics on the
Basis of Direct Inquiry of a Single Expert Regarding
Typical Representatives
2.4 For mali zatio n of Li ng uistic Val ues of C haracteristics
By processing and analyzing the information which can have both qualitative and
quantitative nature, a person makes different decisions. Quantitative
characteristics are those which can be measured. For example, enterprise profits
and losses, age of a person, object weight etc. could be treated as quantitative
ones. Qualitative characteristics cannot be measured in terms of quantities. For
example, some of those characteristics are human appearance, human knowledge,
success of performance of professional duties etc.
Thus, characteristics are mainly described with different "languages": as a rule,
for quantitative characteristics we use usual numbers which are referred to as
physical values of characteristics; for qualitative ones they are words of a natural
