IEEE Systems, Man and Cybernetics Magazine - April 2023 - 11

Fuzzy Evaluation via Fuzzy Interval Numbers
Assume that
Rr ,, ,rr @ represents the set of learnii12iiB
=6
f
er
i's normalized scores on multiple tests, and B denotes
the number of tests. The assessed value of learner i on
cognitive ability is denoted as
V .i Here, we use an interval
number to represent V ,i which is defined as follows:
1) When only one normalized score is taken,
=6
@ where r 1i
and r 2i
maximum normalized scores.
3) When there are more than six normalized scores, the
cloud model theory [38] is used to calculate the fuzzy
interval number.
The calculation method is given in " Calculate Fuzzy Interval
Number via Cloud Model Theory " in " Performing the
Calculations. "
Weight Settings for Evaluation Indexes
Obviously, the five indexes have different importance for
identifying a team leader. The simple average weighting
method is not conducive to accurately synthesizing the
comprehensive ability of a learner. Through a combination
with fuzzy logic, the fuzzy analytic hierarchy
Vr ,.rii i
=6
@
2) When there are fewer than six normalized scores,
Vr ,,r12ii i
denote the minimum and
process (FAHP) overcomes the shortcomings of the traditional
analytic hierarchy process. The FAHP reduces
the influence of subjective factors and avoids the problems
of complicated operation, large computation, and
low accuracy [38].
Evaluation of Learners' Compatibility With Projects
For LC-LTF for project-based learning, we need to calculate
the compatibility between the ability interval numbers
of learners and the ability requirements interval numbers
of the projects. To compare the interval numbers more
accurately, the interval number likelihood formula [39] is
used to compare the ability values with the " expected
intervals " for each ability requirement of the projects.
Assuming that
UU ,ULH
er i's ability that and DD ,DLH
ij
$ is obtained by (1):
PU D$ =
^h
ij
where lU UHL
U iii
i ii @ denotes the interval of learn=6
=6
j
jj@ denotes the expected
interval of this ability in project j, the probability of
UD
minmaxll
ll
UDi
j
,
D jjj
= -
"" ,,UDH
UD
+- j,0
+
i
ij
=- and lD .DHL
Input
Learners
......
Workflow of LTF
Evaluating
Learners or Projects
Modeling Module
Type 1
Modeling Problem
Problem
Identification
Type 2
1) Calculate the Matching
Degree of Learners for Projects
2) Select the Leaders
3) Formulate the Constraints
Forming
Learning Team
CPLEX
Package
Figure 3. The collaborative optimization framework.
April 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 11
Gurobi
Optimizer
Genetic
Algorithm
Clustering
Algorithms
Solving Module
......
1) Select the Leaders
2) Formulate the Constraints
Proficiency
Leadership
Skill
Projects
......
Evaluation Indexes
Learning
Style
Personality
Communication Skill
Process
Evaluation Methods
Query, Pretest, Cloud
Model, ......
Mathematical Tool
Fuzzy Set (FS), IntervalValued
FS, Intuitional
FS, Interval-Valued
Intuitionistic FS, ......
Evaluation Module
Output
(1)
E-CARGO Model
Objective Function
Formulation
E-CARGO Model
Fuzzy
Evaluations
IEEE Systems, Man and Cybernetics Magazine - April 2023

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