Motivation Assessment Model For Intelligent Tutoring System Based On Mamdani Inference System
Motivation Assessment Model For Intelligent Tutoring System Based On Mamdani Inference System
Motivation Assessment Model For Intelligent Tutoring System Based On Mamdani Inference System
Corresponding Author:
Rajermani Thinakaran
Faculty of Data Science and Information Technology, INTI International University
Persiaran Perdana BBN Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia
Email: rajermani.thina@newinti.edu.my
1. INTRODUCTION
The definition of motivation may take several forms and differ upon its application. According to
Keller and Litchfield [1], motivation can be defined as a persons’ desire to pursue a goal or accomplish a task.
Williams and Burden [2] define motivation as a “A state of cognitive and emotional encouragement, which
brings to a firm decision to act, and which gives rise to a period of sustained knowledge and/or physical effort
in order to reach a set of aim or aims”. Motivation has always been important for learning process and has a
great influence [3], [4]. In a real-world classroom, educators easily capture students’ motivation level during
learning process and adjusts lessons accordingly, in order to maximize the student’s interest and participation.
Educators usually understand student motivation level from observational cues such as student body language
or their behavior.
In e-learning environment mainly in intelligent tutoring system (ITS) the same consideration need to
be taken where the tutoring system able to recognize when the student is becoming demotivated. Vicente and
Pain [5] and Thinakaran and Ali [6] have argued that motivation components are as important as cognitive
components in ITS, and that important benefits would arise from considering techniques that track the students’
motivation. Thus, the authors claim that ITS should include a mechanism for detecting the students’
motivational level, and appropriately responding to that level. This study tries to address aforesaid issues by
proposing a model for motivation assessment in ITS that takes the active and successive environment of
motivation into account.
3. METHOD
In this study a deductive approach is used to reach a logical true conclusion [11]. The approach holds
a theory and based on it, make a prediction of its consequences. Figure 1 illustrated how the study carried out
using the deductive approach.
The proposed motivation assessment model was design base on a well-known self-efficacy theory by
Bandura [12], a Canadian psychologist. He has claimed that self-efficacy beliefs effect on choice of activities
a student takes part in; the level of student effort expended in performing a task, persistence in the face of
difficulties in completing a task, and student performance in the task. Through research on self-efficacy as
learning motivations factor, many scholars have demonstrated their relationship. For example, Emre and
Ayverdi [13]; Durak et al. [14]; Gorson and O'Rourke [15], had state that individuals with a high perception
of self-efficacy on a particular situation strive to accomplish a task. They do not easily give up and are persistent
and patient. While Hattie [16], from 800 meta-analyses, the researcher has identified self-efficacy as the
strongest predictor of educational achievement.
Base on self-efficacy theory as motivation factor, choice of activities, effort, performance and
persistence were identified as motivation attributes. These motivation attributes were used in this study to
determine students’ motivation level. Choice of activities is defined as the level of challenging task the student
chooses [17]. Difficulty level of tasks such as low, medium, high, has been considered as a parameter to
measure choice of activities [18]. Effort define as the amount that the student is employing their self in order
to perform the learning activities [19]. To measure effort, the amount of time spent to perform a task [20] has
been considered as a parameter. Performance explains the student’s achievement on a specific topic [21]. To
measure performance, the number of correct answers has been considered as parameter [17], [21]. Persistence,
describe as a constant in performing an activity [21]. The number of questions skipped was used as a parameter
to measure persistence [17], [20].
Fuzzy logic (FL) as artificial intelligent technique applied to predict the students’ motivation level.
This technique was introduced by Zadeh [22] and used when conventional logic fails. It is a computational
paradigm which is based on human thinking. The aim of using FL technique in this study is to capture the
vagueness of effort, performance, choice of activities and persistence, then determine students’ self-efficacy
which are used together to draw the conclusion of students’ motivation level. The main advantage of FL is that
it uses reasoning that closely resembles human. Furthermore, motivation is characterized by ambiguity thus
difficult to quantify. Consequently, Wang and Hsieh [23] suggested the use of FL technique to help in solving
this problem.
In general FL technique consist of [24]: i) fuzzification which translates crisp (real-valued) inputs into
fuzzy values; ii) rule evaluation is an engine that applies a fuzzy reasoning mechanism to obtain a fuzzy output;
and iii) defuzzification which translates this latter output into a crisp value. There are 3 different inference
system which are widely used in FL which are Mamdani inference system [25], Sugeno inference system [26]
and Tsukamoto inference system [27]. The most widely used system is Mamdani inference system [28]. This
inference system also known as Max Min inference system which was introduced by Professor Ebrahim
Mamdani from London University [25]. The advantages are, it is intuitive; it has widespread acceptance, and
Motivation assessment model for intelligent tutoring system based on … (Rajermani Thinakaran)
192 ISSN: 2252-8938
it is well suited to human input. Hence, in this study Mamdani's Fuzzy inferences system as students’
motivation prediction technique was applied.
4. PROPOSED MODEL
To assess students’ motivation level, the authors has applied Mamdani's fuzzy inferences system. The
main advantage of Mamdani's fuzzy inferences system is that it uses reasoning that closely resembles the
presence of human. The aim of using Mamdani's fuzzy inferences system in this study is to capture the
vagueness of effort, performance, choice of activities and persistence which will therefore determines students’
self-efficacy to draw a conclusion on students’ motivation level. The following are steps describes how the
motivation assessment model was developed based on Mamdani fuzzy Inference System.
Effort (EF) parameters depends on the time (t) taken by a student to answer a set of tutorial questions.
The maximum time depends on the time that the teacher has defined for solving a set of questions. For this
study an average of 1.2 minutes is given to answer each question. As in (2) is used to calculate time taken by
the student for answering the given questions. The time taken becomes a crisp value for EF.
Performance (PF) parameter depends on the number of correct answers answered by the student on
the particular set of tutorial questions. As in (3) is used to calculate total number of correct answers (cAns)
answered by the student over the total number of generated questions (numOfQuest) by the system times by
100%. The percentage of correct answers (%cAns) will be the crispy value for PF.
∑𝑛
𝑖=1 𝑐𝐴𝑛𝑠𝑖
𝑝𝑒𝑟𝐶𝑎𝑛𝑠 = × 100 (3)
𝑛𝑢𝑚𝑂𝑓𝑄𝑢𝑒𝑠𝑡𝑛
Persistence (PS) parameter depends on the number of skipped questions on a given tutorial. As in (4)
is used to calculated as the total number of skipped questions (sQuest) by the student over number of generated
questions (numOfQuest) by the system times by 100%. The percentage of skipped questions (%sQuest) will
be the crispy value for PS.
∑𝑛
𝑖=1 𝑠𝑄𝑢𝑒𝑠𝑡𝑖
𝑝𝑒𝑟𝑆𝑞𝑢𝑒𝑠𝑡 = × 100 (4)
𝑛𝑢𝑚𝑂𝑓𝑄𝑢𝑒𝑠𝑡𝑛
4.2. Fuzzification
Fuzzification, translates crisp (real-valued) inputs into fuzzy values using a membership function [23].
In this study, triangular and trapezoidal with R- and L- functions were used to translate each linguistic variable
value as crisp value into fuzzy values. The membership functions have proven popular with fuzzy logic and
have been in use extensively due to their simple formula and computational efficiency [24]. The following are
fuzzification for each input linguistic variable.
CA has 3 fuzzy sets shows in Figure 2 with possible values of easy, medium and hard which are
denoted as CA(x)={easy, medium, hard}. These distributions are formulated as in (5).
0, 𝑥 > 0.8
0.8−𝑥
𝐶𝐴𝑒𝑎𝑠𝑦 (𝑥) = {0.8−0.2 , 0.2 ≤ 𝑥 ≤ 0.8 (5)
1, 𝑥 < 0.2
0, 𝑥 < 0.4
𝑥 − 0.4
, 0.4 ≤ 𝑥 < 1.0
𝐶𝐴𝑚𝑒𝑑𝑖𝑢𝑚 (𝑥) = 1.0 − 0.4
1.6 − 𝑥
, 1.0 ≤ 𝑥 ≤ 1.6
1.6 − 1.0
{ 0, 𝑥 > 1.6
0, 𝑥 < 1.2
𝑥 − 1.2
𝐶𝐴ℎ𝑎𝑟𝑑 (𝑥) = { , 1.2 ≤ 𝑥 < 1.8
1.8 − 1.2
1, 𝑥 > 1.8
EF has 3 fuzzy sets shows in Figure 3 with possible values of short, medium and long which are
denoted as EF(x)={short, medium, long}. These distributions are formulated as in (6).
0, 𝑥 > 9.0
9.0 −𝑥
𝐸𝐹𝑠ℎ𝑜𝑟𝑡 (𝑥) = {9.0−3.6, 3.6 ≤ 𝑥 ≤ 9.0 (6)
1, 𝑥 < 3.6
0, 𝑥 < 5.4
𝑥 − 5.4
, 5.4 ≤ 𝑥 < 10.8
𝐸𝐹𝑚𝑒𝑑𝑖𝑢𝑚 (𝑥) = 10.8 − 5.4
16.2 − 𝑥
, 10.8 ≤ 𝑥 ≤ 16.2
16.2 − 10.8
{ 0, 𝑥 > 16.2
0, 𝑥 < 12.6
𝑥 − 12.6
𝐸𝐹𝑙𝑜𝑛𝑔 (𝑥) = { , 12.6 ≤ 𝑥 < 18.0
18.0 − 12.6
1, 𝑥 > 18.0
PF has 3 fuzzy sets shows in Figure 4 with possible values of poor, good and excellent which are
denoted as PF(x)={poor, good, excellent}. These distributions are formulated as in (7).
0, 𝑥 > 40
40 −𝑥
𝑃𝐹𝑝𝑜𝑜𝑟 (𝑥) = {40−20 , 20 ≤ 𝑥 ≤ 40 (7)
1, 𝑥 < 20
Motivation assessment model for intelligent tutoring system based on … (Rajermani Thinakaran)
194 ISSN: 2252-8938
0, 𝑥 < 30
𝑥 − 30
, 30 ≤ 𝑥 < 50
𝑃𝐹𝑔𝑜𝑜𝑑 (𝑥) = 50 − 30
70 − 𝑥
, 50 ≤ 𝑥 ≤ 70
70 − 50
{ 0, 𝑥 > 70
0, 𝑥 < 60
𝑥 − 60
𝑃𝐹𝑒𝑥𝑐𝑒𝑙𝑙𝑒𝑛𝑡 (𝑥) = { , 60 ≤ 𝑥 < 80
80 − 60
1, 𝑥 > 80
PS has 3 fuzzy sets shows in Figure 5 which are low, medium and high and are denoted as PS(x) =
{low, average, high}. These distributions are formulated as in (8).
0, 𝑥 > 40
40 −𝑥
𝑃𝑆𝑙𝑜𝑤 (𝑥) = {40−20 , 20 ≤ 𝑥 ≤ 40 (8)
1, 𝑥 < 20
0, 𝑥 < 30
𝑥 − 30
, 30 ≤ 𝑥 < 50
𝑃𝑆𝑎𝑣𝑒𝑟𝑎𝑔𝑒 (𝑥) = 50 − 30
70 − 𝑥
, 50 ≤ 𝑥 ≤ 70
70 − 50
{ 0, 𝑥 > 70
0, 𝑥 < 60
𝑥 − 60
𝑃𝑆ℎ𝑖𝑔ℎ (𝑥) = { , 60 ≤ 𝑥 < 80
80 − 60
1, 𝑥 > 80
The output variable which is called as motivation level (ML) of a student is also determined by the
fuzzy logic. The motivation level of a student has three fuzzy sets shows in Figure 6 which are low, medium
and high and are denoted as ML(x) = {Low, medium, high}. These distributions are formulated as in (9).
0, 𝑥 > 1
1 −𝑥
𝑀𝐿𝑙𝑜𝑤 (𝑥) = {1−0.5 , 0.5 ≤ 𝑥 ≤ 1 (9)
1, 𝑥 < 0.5
0, 𝑥 < 0.75
𝑥 − 0.75
, 0.75 ≤ 𝑥 < 1.5
𝑀𝐿𝑚𝑒𝑑𝑖𝑢𝑚 (𝑥) = 1.5 − 0.75
2.25 − 𝑥
, 1.5 ≤ 𝑥 ≤ 2.25
2.25 − 1.5
{ 0, 𝑥 > 2.25
0, 𝑥 <2
𝑥−2
𝑀𝐿ℎ𝑖𝑔ℎ (𝑥) = { , 2 ≤ 𝑥 < 2.25
2.25 − 2
1, 𝑥 > 2.25
Motivation assessment model for intelligent tutoring system based on … (Rajermani Thinakaran)
196 ISSN: 2252-8938
On the other hand, the max method is applied as an aggregation function. The input for the aggregation
process is the list of truncated output returned by the implication process for each rule. Figure 9 shows all 26
rules which are displayed to show how the rule outputs are aggregated into a single fuzzy set whose
membership function is assigned for every output (motivation) value and are represented in a graphical view.
4.5. Defuzzification
Defuzzification functions to convert the fuzzy values into crisp values. The input for the
defuzzification process is the aggregate output. In this study, a Centroid method was applied which is one of
the most common methods used. The Centroid method which returns the center of area under the curve is
shown in Figure 10 in a graphical view. From the example given, the defuzzified value is between 0 and 1.
Therefore, it can be concluded that the students’ motivation level is recorded to be at 0.452 which is considered
to be at a low level.
Motivation assessment model for intelligent tutoring system based on … (Rajermani Thinakaran)
198 ISSN: 2252-8938
Figure 11 display the steps how the motivation assessment model was developed based on Mamdani
Fuzzy Inference System. The steps started with deciding linguistic variables and fuzzy sets; translates crisp
inputs into fuzzy values using a membership function; Fuzzy inferencing; and defuzzification. Following with
motivation assessment algorithm shows in Figure 11 derived from motivation assessment model shows in
Figure 12. While Figure 11 is motivation assessment algorithm derived from motivation assessment model
which was illustrated in Figure 11. Figure 12 as shown in Appendix.
Figure 11. Motivation assessment model based mamdani fuzzy inference system
APPENDIX
BEGIN
start time
//generate 12 mcqs one by one
for (q = 1; q <= 12; q++){
display question
read(ans)
//calculate weightage factor
wfans = (wf * ans) + wfans
if (ans == True) //calculate correct answer
cAns = cAns +1
//calculate number of skipped questions
if (ansSkipp == True)
sQuest= sQuest +1
}
stop time
wa = wfans /12 // As in (1)
t = stop time – start time // As in (2)
perCans = (cAns /12) *100 // As in (3)
perSquest = (sQuest / 12) *100 // As in (4)
/*translates crisp inputs into fuzzy values using membership function*/
CA(x)← difficulty level (wa)
EF(x)← time taken (t)
PF(x)← number of correct answered (perCans)
PS(x) ← number of skipped question (perSquest)
//rules output
(min method) ← 26 rules //implication function
// aggregation function
(max method) ←output of min method on 26 rules
/*Defuzzification is converts the fuzzy values to crisp values */
ML(x)← (Centroid method)
display (ML(x))
END
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BIOGRAPHIES OF AUTHORS
Ir. Dr. Malathy Batumalay holds a BEng. (Electrical Engineering) form University
Tun Hussein Onn, MEng. (Telecommunication) from University Malaya and Ph.D. (Photonics)
from University Malaya. Currently she is attached as Associate Professor with the Faculty of Data
Science and Information Technology in INTI International University, Negeri Sembilan,
Malaysia. She focuses on the research of Photonics Engineering, Fiber Optics and Lasers
technology. In her previous research work, she developed fiber optics into sensors to monitor the
relative humidity, temperature and also as biosensor. She is currently collaborating with local
Universities to further enhance the performance of sensors for several applications. She can be
contacted at email: malathy.batumalay@newinti.edu.my.