Information Technology Reference
In-Depth Information
The same set can be written in two ways
{
~
}
A
=
0
2
/
1
0
/
2
0
/
3
0
/
4
;
~
{
}
A
=
0
2
/
1
+
0
/
2
+
0
/
3
+
0
/
4
.
Example 1.6.
Building of fuzzy set on the basis of frequency approach [60—63].
Let us consider fuzzy set
~
= {the raised demand for cars of the German concern
"Volkswagen"}.
Sales volumes of cars of this concern over a certain period are the following:
"Bora" — 75, "Passat" — 120, "Golf" — 90, "Jetta” — 60, “Touareg” — 90. It is
clear that the "Passat" model was in maximum demand. By introducing a
normalization factor 1/120, we'll obtain fuzzy set
~
= {0. 625 / "Bora", 1 /
"Passat", 0.75 / "Golf", 0.5 / “Jetta”, 0.75 / “Touareg”}.
In [64], for building of membership function of fuzzy set the probability density
function of a continuous chance quantity is evaluated over small volume sample.
Membership function for a certain element of universal set can be defined by
ratio of a number of experts considering that this element is typical for fuzzy set,
to a number of all experts who are taking part in a survey [35].
Example 1.7.
Building of fuzzy set on the basis of an expert group survey. Six
independent experts estimated the “correspondence to curricula” characteristic for
seven samples of manuals (1—7). Following outcomes were obtained:
Sample No.
Number of experts giving positive (negative) mark
1
2 (4)
2
4 (2)
3
5 0)
4
1 (5)
5
6 (0)
6
3 (3)
7
0 (6)
Thus, this fuzzy set can be written as
1
2
5
1
1
⎩
⎨
⎧
⎭
⎬
⎫
/
1
/
2
/
3
/
4
1
/
5
/
6
0
/
7
.
3
3
6
6
2
If it is guaranteed that experts are far from random errors, they can be directly
interrogated about values of membership function. It is important to remember
about distortions of evaluations which are expressed rather often in the subjective
tendency to shift them to extremities of an estimating scale [59].
