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In-Depth Information
⎧
1
0
≤
x
≤
0
0665
;
⎪
⎪
⎨
x
−
0
0665
()
⎪
⎪
⎩
μ
x
=
1
−
,
0
0665
<
x
≤
0
1995
;
1
0
133
0
0
1995
<
x
≤
1
⎧
0
x
≤
0
0665
;
⎪
x
−
0
1995
1
+
,
0
0665
<
x
≤
0
1995
;
⎪
0
133
⎪
()
μ
=
x
1
0
1995
<
x
≤
0
2835
;
⎨
2
⎪
x
−
0
2835
1
−
,
0
2835
<
x
≤
0
5845
;
⎪
0
301
⎪
0
0
5845
<
x
≤
1
⎩
0
0
≤
x
≤
0
2835
;
⎧
⎪
x
−
0
5845
1
+
,
0
2835
<
x
≤
0
5845
;
⎪
0
301
⎪
()
μ
x
=
1
0
5845
<
x
≤
0
724
;
⎨
3
⎪
x
−
0
724
1
−
,
0
724
<
x
≤
0
908
;
⎪
0
184
⎪
0
0
908
<
x
≤
1
⎩
⎧
1
0
≤
x
≤
0
724
;
⎪
⎪
⎨
x
−
0
908
()
⎪
⎪
⎩
μ
x
=
1
+
,
0
724
<
x
≤
0
908
;
4
0
184
0
0
908
<
x
≤
1
Graphs of the obtained membership functions are shown in Fig. 2.4. a.
Example 2.2.
Model-building of COSS “knowledge of students”.
There are data of progress of 100 students of a certain specialty over a certain
period of time
Mark
Number of students
E ("unsatisfactory”)
10
C ("satisfactory”)
40
B (“good”)
30
A (“excellent”)
20
Let us construct COSS “knowledge of students” with terms "E”,"C”, "B”, "A" and
membership functions
()
()
() {
5
μ
x
—
μ
x
, accordingly.
. Based on
T
x
=
2
3
4
~
~
values of relative frequencies, we obtain:
⎧
1
0
≤
x
≤
0
05
;
⎪
⎪
⎨
x
−
0
05
()
⎪
⎪
⎩
μ
x
=
1
−
,
0
05
<
x
≤
0
15
;
~
0
0
0
15
<
x
≤
1
