Information Technology Reference
In-Depth Information
•
Based on updates of the KL(Ci)
j
), the KL(C
i
) is deteriorated according to:
R7:
If KL(Ci)
=
FS
n
with
μ
FSn
(Ci)
=
1
, then it does not change
R8:
The formula
X
I
=
1
−
µ
D
C
I
,
C
J
∗
X
I
+
MIN
[
µ
D
C
I
,
C
J
∗
X
I
,
µ
D
∗
X
J
]
, where x
i
and x
j
are the values of the criterion, which determines
the fuzzy sets that are active each time for Ci
i
and C
j
respectively, is used (for
the calculation of previous xi,
i
, the membership value of the upper active fuzzy
set is used). Then, using the new xi,
i
, the KL(C
i
) is determined, calculating the
membership functions.
•
Limitation:
C
I
,
C
J
µ
FSi
=
1
2.4.1 Integration of the Fuzzy Rules
The application of the fuzzy rules of the step 3 that was described above deals
with the problem of estimating wrongly the knowledge level of a domain con-
cept. In particular, consider the fuzzy sets {“Uknown”, “Known”, “Well-Known”,
“Learned”} and the set of their membership functions (
μ
Un
,
μ
K,
μ
WK
,
μ
L
) that
represent the student's knowledge level of a domain concept. Let's the domain
concept C
i
to be 100 % 'Learned' and the “strength of impact” of Ci
i
on the fol-
lowing concept Ci
j
to be 0.3. The knowledge level of C
j
is 100 % 'Unknown'.
According to the rule R2, the knowledge level of C
j
will become 30 % 'Learned'.
However, that it means that the rest 70 % of the concept C
j
is 'Known'? The
answer is no. The rest 70 % of the C
j
can be 'Unknown', 'Known', 'Well-Known'
or 'Learned', or different parts of it can belong to a different fuzzy set (i.e. 10 %
'Unknown', 20 % 'Known' and 40 % 'Well-Known'). In addition, let's the set that
describes the knowledge level of the domain concept Ci
i
to be (0.8, 0.2, 0, 0) (e.g.
80 % 'Unknown' and 20 % 'Known'
ₒ
KL(C
j
)
=
0.2 'Known') and the “strength
of impact” of Ci
i
on its following concept Ci
j
to be 0.6. The knowledge level of Ci
j
is
20 % 'Learned'. According to the rule R4, the knowledge level of C
j
will become
60 % 'Known'. However, that it means that the rest 40 % of the concept C
j
is
'Uknown'? The answer is no. It can be any of the above fuzzy sets.
A solution to this problem is to keep data for each domain concept of the
learning material concerning the different part of the particular concept that can
be affected be other related concepts. In such a way, the system can be informed
each time about the knowledge level of each separate part of the particular domain
concept and it is able to draw conclusions about the learner's knowledge level on
the overall domain concept. For example, according to the Fig.
2.10
(Sect.
3.1
)
the domain concept C
12
is affected by both concepts C
11
and C
6
. Initially
is KL(C
6
)
=
KL(C
11
)
=
KL(C
12
)
=
100 % 'Uknown'. During the learning
process, the concept C
6
is delivered to the learner firstly. The learner's knowledge
level on the particular concept becomes 20 % 'Well-Known' and 80 % 'Known'
(KL(C
6
)
=
20 % Well-Known). According to the rule R2, the learner's knowl-
edge level on the domain concept C
12
will become 7 % 'Well-Known' and 28 %
'Known'. The other part, however, of C
12
is not affected by C
6
. So, its knowledge
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