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1
[
()
()
]
min
μ
x
,
μ
x
dx
i
n
i
n
β
=
0
,
i
=
1
n
=
1
N
.
1
[
]
()
()
max
μ
x
,
μ
x
dx
i
n
(5.34)
0
= , the state of n -th object is defined by p -th by level of scale
Y = “extremely unsuccessful”,
β
p
n
max
β
i
n
If
i
Y =”unsuccessful”, Y = “mean successful”,
Y = "extremely successful",
Y = "rather successful",
p .
Let us denote ratings of n -th object for phases 1 and 2 with
=
1
A ,
1
2
A accord-
1
A to
A , it is possible to draw the following con-
2
ingly. Depending on ratio of
, the state of n -th object is worsened; if
1
2
A
1
>
A
2
A
<
A
clusions: if
the state of
n
n
n
n
1
2
n -th object is improved; if
A
=
A
, the state of n -th object is unchanged.
n
n
5.6 Examples of Practical Application of the Methods
Developed
Example 5.1. Obtaining of rating points of trainees through their academic achieve-
ments during a semester. Rating systems of knowledge evaluation are widely applied
in educational process and play an essential role in the education quality control as-
pects. These systems allow, at any grade level, obtaining accessible and opportune in-
formation in the form of some integral index used for making some administrative
decisions. Rating systems of knowledge evaluation are purposed for lowering the
subjectivity between teachers and trainees, and also to eliminate other (probably
latent) coefficients hindering to objectively evaluate level of training.
Let us consider a problem of obtaining rating points of knowledge of students
through their academic achievements during a semester. Calculation-graphic tasks
(CGT) and tests (T) in linear algebra, analytical geometry and following sections
of mathematical analysis: limits, derivatives and indefinite integrals, were esti-
mated with marks from zero to ten points. In addition, independent work and
class-work were evaluated with marks from zero to ten points. Let us assume that
all types of educational activities have equal weight coefficients. Results of an
evaluation of knowledge of ten trainees are shown in Table 5.1.
Using the method described in §2.2, COSS "knowledge of students studying
higher mathematics” is constructed. Data necessary for model-building are ob-
tained on the base from information avail abl e in the previous experience of a
teacher. Membership functions
()
l of term-sets "F", “C”, “B”, “A”,
accordingly, are membership functions of T
μ
x
,
=
1
4
l
numbers or normal triangular
numbers and have parameters
() (
)
() (
)
μ
x
=
0
0
0
0
2
;
μ
x
=
0
0
0
2
0
2
;
1
2
() (
)
() (
)
μ
x
=
0
0
2
0
2
;
μ
x
=
0
1
0
2
0
.
(5.35)
3
4
 
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