Information Technology Reference
In-Depth Information
a
b
⎧
3
+
1
0
≤
≤
−
3
;
x
x
⎪
⎪
⎨
b
a
()
⎪
⎪
⎩
μ
=
x
3
3
1
b
0
−
3
<
x
≤
1
a
3
⎧
a
b
−
3
x
,
0
≤
x
≤
−
3
;
⎪
b
a
⎪
⎪
3
3
b
1
−
b
()
μ
x
=
1
−
a
x
−
b
,
−
3
<
x
≤
3
;
⎨
1
3
3
a
a
⎪
3
3
1
−
b
⎪
3
0
<
x
≤
1
⎪
a
⎩
On constructing the COSS membership functions for each evaluation
3
y
,
it is possible to determine its degrees of membership to COSS terms and to put in
correspondence that term (or that level of a verbal scale) membership degree of
which exceeds 0.5. Existence of such term for each evaluation
y
is stipulated by
characteristics of COSS membership functions. The related outcomes obtained can
generally not coincide with outcomes of expert preliminary allocations of
evaluations
i
=
1
j
y
to levels of a verbal scale.
Example 2.3. Model-building of COSS “knowledge of students”.
A teacher
ap
pra
ises knowledge of eight students for a certain with two points: the first
x
;
i
is a result of examination and can accept values "F" (“unsatisfactory”), “C”
“satisfactory”), “B” (good”) and “A” (“excellent”); the second,
=
1
8
y
, is a result of
≤
nk
, where
k
is a number of
properly performed tasks,
n
is a number of all tasks performed (Table 2.1).
Let us construct COSS “knowledge of students” with terms
testing and can take discrete values
0
/
≤
1
X
= F,
X
= C,
2
X
= B,
X
= A.
Let us start constructing with membership function
()
μ
x
of term
X
. As to
level “A” knowledge of only two students are referred to, let us join to them
outcomes of the students with level "B", and let us suggest the teacher who carried
out an evaluation to make paired comparisons of knowledge of all four students.
Having arranged serial numbers of students according to the obtained points
4
y
,
we obtain a conditional ordinal series
No. 2, No. 1, No. 4, No. 3.
to which the numerical ordinal series corresponds
0.9; 0.8; 0.7; 0.6.
The teacher makes paired comparisons of knowledge of students from the
conditional ordinal series using Saati scale. The following matrix of paired
comparisons is obtained:
