A Fuzzy Rule Data Base to
Guide and Monitor Student Learning

Kai WARENDORF, Sharon TAN, TSAO Su Jen

School of Applied Science, Nanyang Technological University, Singapore 639798

Abstract. The introduced tutoring system BSS1 is able to monitor the student's progress and strength and weakness by keeping student profile parameters. The system is able to suggest topics/sub-topics the student should embark on next. This is done by a fuzzy logic engine that evaluates five variables and ranks the topics/sub-topics accordingly to the last sub-topic studied by the student. According to the Rank of all sub-topics the tutoring system is then able to chose the subject to be studied next. The topic with the highest rank will be recommended to the student as the next study topic.

1 Introduction

The Brilliant Scholar Series 1 (BSS1) is a tutoring system currently used by several thousand home and school users to learn curricular subjects such as mathematics and sciences in Singapore. It is an AI-based tutoring system using heuristics to interact with users and monitor their progress.

We believe the use of fuzzy logic techniques can improve the performance of such tutoring systems by introducing intelligent features to better manage the student's learning. After studying the general requirements of features required by BSS1, a suitable fuzzy logic model was selected. Based on this model, a general fuzzy logic engine was designed and implemented to support development of intelligent features for BSS1. In order to develop such features, the problem had to be suitably modeled and a knowledge base created, followed by testing and tuning with appropriate procedures.

2 Overview of the Fuzzy Logic Engine

The methodology taken is Fuzzy Logic control which allows human description of the physical systems and the required control of the required control strategy to be simulated in a reasonably natural way. A fuzzy logic controller can be regarded as a real-time expert system that employs fuzzy logic to manipulate quantitative variables. It also provide a means of converting a linguistic control strategy derived from expert knowledge into an automatic control strategy. The approach provides an effective means of capturing the approximate, non-crisp nature of the way we normally describe the real world [1].

As shown in Figure 1, the fuzzy logic control consists of a

Figure 1: Structure of the Fuzzy Logic Engine

3 Rules and Knowledge Base of the Fuzzy Logic Engine

3.1 General Requirements of Intelligent Features for BSS1

BSS1 provides students with a large pool of questions collected from past year examinations. The questions are organized into different topics and sub-topics, and information such as the level of difficulty and expected time needed for each question are available. Some of these past year examination questions have been adapted such that all are multiple-choice questions. BSS1 has a pool of teachers who prepared all the answer choices and also solution hints and notes for each question.

The aim of BSS1 is to help students to manage their learning by testing their knowledge with multiple-choice questions. BSS1 is able to monitor the students' progress, their strengthes and weaknesses by keeping student profile parameters such as the questions attempted, the points scored, the time taken and the performance trend. Together with other information such as the relative importance of topics, their relation to one another, and the period of time left for the student to prepare for his exams, the system should be able to manage the student's learning intelligently, for example, by suggesting topics/sub-topics the student should embark on first.

As can be seen, the problem is not a very structured one, and a human teacher (expert) trying to solve this problem might use intuitive guidelines like "If this sub-topic is very important in the exams, and the student is still weak in it, and he hasn't spent enough time on it yet and the exams are near, then he should embark on it straight away". Such a guideline or rule encompasses a lot of vagueness, for example, how important exactly is very important, or how much time do we mean by not enough. If we try to define all these in a complete and precise manner (in numerical terms), our rules will become very cumbersome, especially when we try to take care of borderline cases differently in order to avoid awkward discontinuities. Fuzzy logic is thus very useful here.

3.2 Criteria used in Choosing Sub-topics

As the ultimate usage of the system is for students taking the "O" Levels, the author has to see the problem from the perspective of an "O" level student. The problem to be incorporated and applied to the engine is to help the student to choose the next sub-topic after he/she has just completed one. Thus, looking at the problem, the authors felt that the following factors, in order of priority are the most important criteria to help the student in choosing the next sub-topic:

3.3 Formulation Of Rules

The rules formulated are broken into 3 groups as shown below (only selected examples of the rules are shown):

In group 1, the objective is to determine the level of importance of the sub-topics in the database. Frequency and Relation are correlated to get an intermediate variable Urgency which gives the urgency of the sub-topics.

Frequency ANDRelation =======>Urgency
Vhigh VhighVhigh
High OkOk
Ok VlowLow
Low VhighOk
Vlow LowVlow

The result of the above rules in correlation with Time will determine the level of Importance of each individual sub-topic in the database.

Vhigh VhighVhigh
High OkHigh
Ok VlowOk
Low VhighOk
Vlow LowVlow

In group 2, the objective is to determine the suitability of possible sub-topics to be chosen.. Similar rules are defined for the variables Relation and Performance.

Relation ANDPerformance =======>Suitability

Group 3 helps to determine if the student had fully understood the sub-topic that he has just completed. The variables used to define this criteria are Completion and Performance.

Completion ANDPerformance =======>Understanding

With the results of the above three groups of rules, namely Importance, Suitability and Understanding, the system is able to select a good sub-topic to be studied next using the Rank of the suggested sub-topics.

Importance ANDSuitability ANDUnderstanding ===>Rank
Vhigh VhighVhigh Vhigh
Vhigh OkHigh High
High VhighOk High
High OkVlow Low
Ok VhighOk High
Ok OkLow Low
Low VhighOk High
Low VlowOk Vlow
Vlow VhighOk Ok

3.4 Fuzzy values of Knowledge Data Base

The database provides the necessary definitions of the fuzzy parameters as fuzzy sets with membership functions defined on the universe of discourse for each variable. Construction of the database involves defining the universe of discourse for each variable, determining the number of fuzzy sets and designing the membership functions. The fuzzy sets defined for input variables in the antecedent of a fuzzy rule form a fuzzy input space with respect to the input universes of discourse, while those in the consequent of a fuzzy rule form the fuzzy output space. They partition the input and output spaces into various allowed fuzzy values. In order to use the above rules, fuzzy values for the knowledge base must be defined.


Figure 2: Input and output universes for sub-topic evaluation

As shown in Figure 2, there are five input universes (Frequency, Time, Relation, Completion, Performance) and one output universe (Rank).

4 Derivation of Sub-topics

The tutoring program will supply the five inputs required for the engine to fuzzify. When the engine is fired, fuzzification , reasoning and defuzzication will be done. The output of the engine would be a crisp value which would be useful for the selection of the next subtopic for the student to attempt (known as the rank).

The implementation of the rules can be best illustrated by an example. Taking the rule shown in Figure 3, we will illustrate how the two rules are implemented in the fuzzy logic engine.

RULE T000

IF (Frequency IS VHigh) AND
((Relation IS VHigh) OR (Relation IS Ok)) AND
(Time IS Ok) AND ((Completion IS VHigh) OR (Completion IS High)) AND
((Performance IS VHigh) OR (Performance IS High))
THEN (Rank IS High);

Figure 3: Example Rule

If the input to the engine, provided by the system is as follows:

Frequency =100Relation = 80 Time = 60
Completion = 100Performance = 70

then the evaluation (Figure 4) of RULE T000 leads to the following output:

Frequency = 0.9Relation = 0.2 Time = 0.8
Completion = 1.0Performance = 0.95

Evaluating the remainder of RULE T000 the above values are combined with AND which the minimum of these values and yields Rank = 0.2

Figure 4: Graphical Illustration of RULE T000

RULE T000 states that Rank IS High and with the value of Rank = 0.2 the fuzzy output is the trapezoid as illustrated in Figure 5. To obtain a crisp value the center of gravity [2] must be calulated which results the value of 75.0 as output

Figure 5: Result of Rank in RULE T000

This calculation is performed with all possible topics and sub-topics. The topic with the highest rank will be recommended to the student as the next study topic.

5 Summary

This paper discusses how fuzzy logic can be used to help students to chose topics/sub-topics to continue their learning process. The introduced tutoring system BSS1 is able to monitor the student's progress and strength and weakness by keeping student profile parameters such as questions which have been attempted (Completion) and the points scored (Performance). Together with other information such as their relation to one another (Relation), and the period of time left for the student to prepare for his exams (Time), the system is now able to suggest topics/sub-topics the student should embark on next. This is done by a fuzzy logic engine that evaluates five variables and ranks the topics/sub-topics accordingly to the last sub-topic studied by the student. According to the Rank of all sub-topics the tutoring system is then able to chose the subject to be studied next.

Acknowledgments

We like to thank Rajat Kumar Das, Managing Director of Brilliant Systems Pte Ltd and Prof. Wang Peizhang, Formerly Research Staff of the Institute of Systems Science (ISS) to come up with this approach of student monitoring. Further we like to thank Joel Loo Peing Ling, Research Staff at ISS for his encouraging support.

References

[1] Cox, E., "The fuzzy systems handbook: a practioner's guide to building, using, and maintaining fuzzy systems", AP Professional, Boston, 1994

[2] Dubois, D. and Prade, H., "Fuzzy Sets and Systems", Academic Press, NY, 1980