IEEE Systems, Man and Cybernetics Magazine - April 2023 - 14

Table 3. The abilities of learners.
u1
u2
s1
s2
s3
s4
s5
s6
s7
s8
s9
[0.48,0.59]
[0.48,0.59]
[0.51,0.66]
[0.55,0.68]
[0.47,0.57]
[0.55,0.66]
[0.52,0.66]
[0.58,0.69]
[0.41,0.55]
[0.51,0.6]
[0.41,0.52]
[0.48,0.58]
[0.56,0.65]
[0.47,0.56]
[0.52,0.65]
[0.51,0.57]
[0.56,0.65]
[0.38,0.5]
Table 4. The comprehensive
compatibility matrix.
s1
s2
s3
s5
s7
s9
g1 (s8)
0.777
0.919
0.578
0.952
0.601
1
g2 (s4)
0.677
0.853
0.493
0.916
0.523
1
Table 5. The conflict constraints.
s1
s1
s2
s3
s4
s5
s6
s7
s8
s9
s2
s3
1
1
s4
1
s5
Table 6. The results of LTF.
Team
Leader
g1
g2
g3
s8
s4
s6
s6
s7
1
s8
s9
1
g3 (s6)
0.654
0.772
0.5
0.799
0.459
0.99
After that, several learners can be
u3
[0.55,0.58]
[0.52,0.64]
[0.6,0.61]
[0.58,0.62]
[0.51,0.63]
[0.59,0.63]
[0.61,0.61]
[0.55,0.6]
[0.35,0.51]
u4
[0.59,0.61]
[0.38,0.45]
[0.56,0.61]
[0.55,0.55]
[0.35,0.49]
[0.57,0.57]
[0.58,0.61]
[0.55,0.6]
[0.36,0.48]
u5
[0.57,0.58]
[0.45,0.55]
[0.57,0.61]
[0.54,0.55]
[0.49,0.53]
[0.41,0.47]
[0.51,0.58]
[0.55,0.60]
[0.37,0.42]
selected as leaders based on their
abilities. For example, we first set the
expectation intervals of leadership
and communication abilities as [0.5,
0.56] and [0.55, 0.58], respectively, and
filter out unsuitable learners based
on their compatibility calculated by
(1). By utilizing the FAHP method,
suppose the weight values are set as
0.6, 0.1, 0.1, 0.1, and 0.1, respectively.
Then, we sum other abilities with the
weights to obtain the comprehensive
ability of each learner, pick the top
three learners as learning team leaders,
and obtain the set of selected
team leaders
Hs ,, .ss
= " 84 6
,
Taking each leader as the center,
we iteratively calculate the compatibility
between each leader and the other six learners on
five ability metrics via (1). Then, we sum the compatibility
with the preceding weights to obtain the overall compatibility.
The comprehensive compatibility matrix Q is presented
in Table 4.
Considering that there might be conflicts among learners
who might not be suitable for assignment to the same
team, we define a conflict constraint matrix
C ,Q
is presented in " TQ
Learning. " The maximum value of the objective function is
4.59. The formed teams are listed in Table 6.
LC-LTF for Project-Based Learning
Suppose there are nine learners and three projects in a project-based
practical course. Define that
= " gg
Ss ,, ,ss , is
= f 9
" 12
the set of learners, Gg ,, , is the set of projects,
and that there are seven ability metrics, including c1 (i.e.,
Java programming), c2
123
(i.e., Python programming), c3
(i.e., C programming), c4 (i.e., leadership), c5 (i.e., communication
skill), c6 (i.e., learning style), and c7
(i.e., personality).
The assessment results of the learners' abilities are
presented in Table 7.
Suppose
g ,2
c ,1
for g ,1
c ,2 and c3
and g ,3
is defined in Table 8.
are the cognitive ability metrics
respectively, and their expectation
intervals are [0.45, 0.54], [0.43, 0.51], and [0.4, 0.5]. The compatibility
between learners and projects can be calculated
via (1), and conflict matrix CA
Since the ability metrics for each project may be differMembers
s2,
s7
s5, s9
s1, s3
ent, we define a comprehensive ability value to assess
each learner's overall ability for each project. For example,
for leader selection, we suppose that the expectation intervals
of leadership and communication skill are [0.4, 0.46]
and [0.45, 0.48], respectively, and filter out learners with a
compatibility lower than 0.4 via (1). Then, we calculate the
compatibility on cognitive ability and learning style via (1)
and get the weighted sum of the two abilities to obtain the
14 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE April 2023
which is
in Table 5. Then, the optimal solution is gained via CPLEX,
and TQ
for LC-LTF for Course-Based
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