IEEE Systems, Man and Cybernetics Magazine - April 2023 - 12

Performing the Calculations
Calculate Fuzzy Interval Number via
Cloud Model Theory
The three numerical features of a cloud model related
to learner i in cognitive ability are computed by the
reverse cloud generator [37]. Since the number of
scores determines the accuracy of the numerical
features, based on previous research [38], the threshold
number is selected as six. The three numerical features
of a cloud model are obtained as follows:
Z
]
]
]
]
[
\
]
]
]]
Ex
i
i =
En
H =
E
i
1
2
B
B
#|rib
b 1
=
r # | rEx
B =b 1
1
ib - i
B -1 =b 1
1 |^ ib--^
B
rE Enh2
xh2
i
i
where B denotes the number of tests and rib
represents
the score of learner i on test b. The assessed value of
learner i on cognitive ability is defined as follows:
VE EH
VE EH
)
where VH
H
L
ii
x
ii
=+ +
=- -
x
n
i
n
i
E
i
E
i
#
#
c
c
i is the upper bound of V ,i VL
and has a range of 0.1-0.2 [38].
TQ for LC-LTF for Course-Based Learning
R
TQ =
S
S
S
S
S
S
S
S
S
S
S
S
T
TA =
S
S
S
S
S
S
S
S
S
S
S
S
T
1
1
1
1
1
1
1
1
1
1
1
1
V
W
W
W
W
W
W
W
W
W
W
W
W
X
TA for LC-LTF for Project-Based Learning
R
V
W
W
W
W
W
W
W
W
W
W
W
W
X
TM for LC-LTF for Project-Based Learning
R
TM =
S
S
S
S
S
S
S
S
S
S
S
S
SS
T
10 0
01
01 0
00 1
10
10
10
V
00 1
01
W
W
W
W
W
W
W
W
W
W
W
W
WW
X
where m and n represent the number of learners and
learning teams, respectively. Here, ,,Ti j 01
whether learner i is assigned to team j, and Tji ,
Q66!@@ denotes
Q6 =@
6 =@
1
if learner i is assigned to team j; otherwise, ,.Ti j 0
Q
Ti , jQ
6
.
@ satisfies the following constraints:
TH ,,
Q jj n11j
n
| 6 ^h@Ti ,,Q ji m11= ##
j =1
m
| 6 ^h@Ti ,,Q jL jn1
i 1
= ##
j
=
12 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE April 2023
(5)
6 ^h@= ##
(3)
(4)
bound of V ,i and c is the influence coefficient of Hi
i is the lower
E
B
Modeling Module
After obtaining learners' abilities in various aspects,
the E-CARGO model can be adopted to accurately
model the two types of LC-LTF problems in different
application scenarios.
Modeling LC-LTF for Course-Based Learning
For the problem of LC-LTF for course-based learning, to
guarantee the optimal overall effect and quality of learning,
the proposed modeling strategies are as follows:
1) Set different evaluation metrics based on the features of
different courses to obtain a list of candidates for selecting
team leaders. For example, leadership and communication
ability are usually the evaluation metrics for
selecting team leaders. The cognitive ability of learning
team leaders should also be considered since leaders
with high cognitive ability could give fast and accurate
responses to problems proposed by their team members,
and this could motivate interactions and improve
the quality of collaborative learning.
2) Select the top n learners as team leaders, and the set of
leaders is denoted as
HH ,, ,,12 n
f
the number of teams and Hj
jth team.
= " HH , where n is
represents the leader of the
3) Calculate the compatibility between the leader and
other learners on each evaluation metric. Then, obtain
the weighted sum of the compatibility metrics to get the
comprehensive compatibility between the leader and
other learners, denoted as the Q matrix, ,,Q 01 mn
!6
.
@ #
where n is the number of leaders and m is the number
of overall learners. When there are many evaluation
metrics, the FAHP method is used to calculate the
weight values.
4) Define the conflict matrix among learners as CQ
" 01 mm#
,,
Ci ,.i @=12 0
Q
ers. Here, Ci , i @ means that it is not suitable to
assign learner i1
6
6
12 1
=
and i2
to the same team; otherwise,
5) Utilize E-CARGO to model the LC-LTF for course-based
learning based on matrix CQ
and matrix Q and consequently
get the following objective function:
.
m
n
max ,,Qi jT ij
1
66
#
i =1 j =
t=|| @@ (2)
Q
!
, where m denotes the number of overall learnQ
IEEE Systems, Man and Cybernetics Magazine - April 2023

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