A FUZZY
LOGIC APPLICATION IN VIRTUAL EDUCATION
Thiago Drummond Moreira
Universidade CEUMA, Brazil
Email: thiagodr@gmail.com
Maria Augusta Soares Machado
Faculdades IBMEC  RJ, Brazil
Email: mmachado@ibmecrj.br
Submission: 02/07/2014
Revision: 16/07/2014
Accept: 10/11/2014
ABSTRACT
Traditionally, the teaching and
learning process uses the problems resolving for fixing, transmitting and
evaluating concepts and knowledge about a subject. Learning is the process of
acquiring relative permanent changes in understanding, attitude, knowledge,
information, capacity and ability through experience. A change can be decided
or involuntary, to better or worsen learning. The learning process is an
internal cognitive event. To help this teaching and learning process, it is
important the use of a computer tool able to stimulate these changes. Also, it
is important that it can function as validation and helping tool to the
student. These functions are performed by computer systems called Intelligent
Tutoring Systems. This paper describes the use of artificial intelligence
techniques as a teaching support tool. Using Intelligent Tutoring Systems and
fuzzy logic, this work shows, through electronic ways, teaching will be more
efficient and more adapted to students necessities, in group or individually.
Keywords: Fuzzy
Logic, Intelligent Tutoring Systems, Teaching and Learning.
1. INTRODUCTION
Educational
applications using the computer technology have been developed since the 60s.
Initially, they were classified as ComputerAssisted Instruction and used the
paradigm of programmed instruction, whose educational methods feature a focused
exhibition in the form of a teacher. First, the students must understand the
lesson given by the teacher to then answer any questions and, thus, strengthen
their understanding. It means that, teaching can be readily caused by
"schedules of reinforcement", that is, compensating for the behavior
data desired time.
Over
time, the theoretical perspectives of educational psychologists tended to
migrate to cognitive psychology. According to Piaget (1973), most of what one
learns is on their own initiative and in interaction with the reality that
surrounds them. The students build their knowledge. This trend is also seen in
the process of developing these CAI systems.
With
the development of Artificial Intelligence (AI) techniques and research in the
field of cognitive sciences, increased the degree of "intelligence"
of CAI systems. They are named as ICAI ("intelligent" CAI) and later
known as Intelligent Tutoring Systems. One of the main motivations for research
in Artificial Intelligence in Education is the development of principles by
which computational learning environments can be designed as places where
students can have experiences that are essential and beneficial to them,
regardless of their individual differences, experiences previous or other
cognitive situations.
Thus,
by modeling or mapping the students, these systems can customize the
instruction, aligning the presentation with the level of students’ knowledge
and their learning content. Therefore, most systems with these characteristics
present educational methods that provide a way of finding studentcentered
dialogues and tutorials which are basically determined by the conceptual knowledge
and the learning behavior of the students (PARK, 1987).
Figure 1: Field of
intelligent tutoring applications
Currently,
it is accepted that any system that has as its main objective the teaching
function should incorporate principles of AI. These systems need to know the
level of expertise of its members, and recognize which points in the domain of
knowledge the student has evolved and which remains their weak points.
1.
INTELLIGENT TUTORING
SYSTEMS
Expert
systems are computer programs designed to acquire and make available the
knowledge of a human expert. Intelligent tutoring systems (ITSs) are expert
systems applied to education which aim to assist student learning by simulating
a tutor.
According
to Fowler (1991), the ITSs are computer programs for educational purposes and
incorporate AI techniques, usually using the technology of expert systems. The
ITSs are derived from CAI programs and offer advantages over these because they
can simulate the process of human thought within a given area, to assist in
strategies in problem solving and in decision making.
Classified
in accordance to Pozzebon and Barreto (2002), Intelligent tutoring systems
derived from CAI programs (Computer Aided Instruction), which try to implement
a generic model that can be used to teach any student.
In
researches of any educational system involving principles of AI, the approach
is somewhat different from that of the knowledge engineering in which the
experts should represent, in a given domain, their strategies and decisions in
the form of programs. Instead, the main purpose is to capture the knowledge
necessary to enable experts compose an educational interaction. Instead of a
decision, the result of knowledge is knowledge which itself is explicitly
represented so it can be used. Therefore, it is also the responsibility of
programs to compose educational interactions dynamically.
According
to Jonassen (1993), ITSs must pass three tests before being considered
"smart":
·
The content of the topic or skill should be coded so
that the system can access information, make inferences or solve problems.
·
The system should be able to evaluate the acquisition
of this knowledge by the student.
·
Tutorial strategies should be designed to reduce the
discrepancy between expert knowledge and knowledge of the student
It
can be observed:
"[...] ITS are programs that modify their
knowledge bases, realize interventions in the students learning and are endowed
with the capacity to learn and adapt their teaching strategies through
interaction with the students." (Cited by SCHMITZ VACCARI; LÓPEZ; FARACO;
ROSATELLI, 2002, p. 3).
The
ITSs are formed basically by four modules.
First
Module  The model of the expert or domain model contains the
stored expert knowledge on the subject being taught. This knowledge is acquired
from an expert and should therefore be transferred to the students (SCHMITZ et.
al., 2002). It is fundamentally a knowledge base containing information for a
particular domain, which is organized in any way to represent the knowledge of
an expert or teacher (POZZEBON; BAKER, 2002).
Second
Module  The model of the guardian or pedagogical model is
responsible for adopting different ways to expose a subject, making it
understandable and interesting. In the statement of a body of knowledge to a
person, different strategies and techniques are selected and dynamically
combined in response to the attitudes and needs of students (POZZEBON; BAKER,
2002).
Third
Module  The student model contains the information for each
student who uses the system. This information is related to the level of
student knowledge on the subject and their rate of learning (SCHMITZ; LOPEZ;
ROSATELLI FARACO, 2002). The main feature of this model should include all
aspects of knowledge and behavior student bring consequences for their
performance and learning (POZZEBON; BARRETO, 2002). Perhaps, this is the most
important module of an ITS. It is from the information contained in this model
that all strategies, contents are exposed to tutor students through the model.
Fourth
Module  The interface module is the communication channel
between the ITS and the student (SCHMITZ et. al., 2002). In software
engineering, the user interface has been the primary concern of designers when
they are discussing the creation of a new application because, as stated by Hix
and Hartson, "For users, the interface is the system itself." (POZZEBON;
BARRETO, 2002).
Figure 2: Basic
architecture of an ITS
Through
this architecture, it can be seen that the student has a greater chance to have
a personalized learning. It will be up to the teacher to ask questions,
perchance not solved by ITS, and support the student. Some advantages of
intelligent tutorial systems could be:
“First, the computer finds it easier to retain the
information and deliver it in a systematic, thorough and complete manner. The
computer never forgets a detail, if this is specified in the program. A
headache or a family problem never changes its performance. Second, this
capability allows systematization of computer monitoring of the student in
relation to the most frequent errors and the execution the tasks orders. Often
the teacher has a lot of difficulty in performing this monitoring, so it can be
done at a much more comprehensive way by the computer. Third, computer systems
today have many multimedia features such as colors, animation and sound.” [...]
(VALENTE, 1997, p. 20).
2.
MULTIAGENT
INTELLIGENT TUTORING SYSTEMS
For
distance learning, some authors claim that this is responsible for a mass
without quality education. As has been seen, the intelligent tutoring systems
are especially important in the customization of teaching the student. By
joining this idea of Internet’s ITSs, it can cause distance learning with
higher quality. It is necessary to think of a new architecture of intelligent
tutoring systems which can be individualized to the needs of each student and
also be collective and collaborative with other learners.
An
agent can be defined as an entity (human or artificial) physical or abstract
that performs an action on something, either about the students or their
environment, producing an effect (FERBER apud SICHMAN, 1992).
In
this environment, students are divided into distinct environment in which areas
are called cooperative groups. Basically, two types of interactions occur,
intragroup interaction, where students learn by interacting and cooperating
within their own groups with artificial agents and the teacher, and intergroup
interaction that can occur between practitioners in various existing groups.
These interactions occur through the use of multimedia and networks, intranets
and internet technology.
The
description of the architecture of a multiagent learning environment is:
Tutor
Agent  participates in all the activities of teaching and
assessment. It controls the interactions of groups with the system during the
process of teaching / learning. It is also responsible for presenting the
knowledge to learners.
Domain
agents  are holders of certain knowledge, an expert. It is
responsible for the storage and representation of specific knowledge, which is
the only feature that differentiates one from another Domain Agent.
Modeling
agents  responsible for the acquisition, representation and
maintenance of the information about students and groups during the process of
teaching / learning process.
Strategic
agent  is responsible for defining pedagogical strategies
to be adopted by the Tutor Agent from interaction with Modeling Agent, and
after observing the behavior of each learner, that is, who decides what, when
and content that will be presented to the students.
Agent
Search  aims to provide the learner custom that can help
you clear the doubts information. A set of intelligent mobile agents is
instantiated to access remote data resources.
Teacher
agent is a human agent noted for performing the roles of supervisor,
evaluator and specialist.
Students’
agents  are the users’ target of the system. The good
performance of them is the target to be reached.
Knowledge
Engineer agent  is responsible for maintaining the Domain Agent,
which includes the issue of knowledge of each organization and their domains.
Figure 3: ITS
Architecture Multiagent
3.
FUZZY LOGIC
About
2000 years ago, the use of Boolean logic (where an expression can only take two
values, true or false) was a way of modeling mathematical problems.
Conventional computer modeling uses this concept of ambivalence and therefore
cannot work with ambiguities (MUKAIDONO cited by COSTA et al., 2003, p. 1).
This
kind of modeling (can be written as reasoning), assuming a statement as true or
false, is impossible when thinking about realworld problems. It is hard to
imagine (if not impossible) for a person considering only two possibilities
(yes / no, true / false, black / white) when dealing with factors such as
ambiguities, uncertainties and vague information.
Trying
to approximate the mathematical modeling and realworld problems, Zadeh
recognized the many possibilities between true and false (after observing that
many rules used by people to make inferences could not be explained by the
people who used) and developed in 1965, a variation of traditional logic and
fuzzy logic.
Different
from Boolean logic, fuzzy (or diffuse)
is a multivalued logic  instead of an element being 100% owned by one set or
the other or a proposition wholly true or false, fuzzy logic works with
partially true statements and partially false at the same time. In this
context, Boolean logic becomes a particular case of fuzzy logic (BARBALHO,
2001, p. 20).
As
an example, one can present the problem to identify people with average height.
If we consider such people with a height between 1.60 and 1.70 meters, Boolean
logic could not identify the people with 1.59 meters as belonging to this
group. Already fuzzy logic identifies that person as belonging to the group,
but with a lower degree of certainty that another person with 1.65 meters.
Therefore,
one can define fuzzy logic as a tool capable of capturing vague information,
generally described in natural language, and convert them to digital form for
easy handling (WAGNER cited by COSTA et al., 2003, p. 3). The goal is to
capture the different degrees of existing truth for real life situations and
model them in a mathematical form.
3.1.
Fuzzy Sets
In
classical set theory, the sets are defined as a collection of objects that have
certain characteristics in common. These objects can be numbers, words,
concepts, anything and have only two ways of relating to the set: either belong
or not belong to the set.
When
analyzing the problem of an average stature, one can see that people with 1.59
or 1.71 meters do not belong to the group of people with average height, since
this set includes only people with heights between 1.60 and 1.70 meters.
Although for obvious reasons, they must belong to this set.
Zadeh,
to formulate the fuzzy set theory, was based on the classical theory of sets
and presents that as a generalization of this. The sets are also defined on a
domain (Universe of Discourse), but differ from those for not having a clearly
defined boundary (apud BARBALHO; ZADEH, 2001, p. 20). It tries to translate,
through formal mathematical representations, the inaccurate information from
the real world.
The
central idea is that an element belongs to a set with a certain degree of
membership. In theory, this degree is presented as a Function of Relevance.
This function maps each element of the universe with a number between 0 and 1
(in the classical theory, the degree of membership takes only the values 0 or
1). Thus, propositions are not only true or false, but range from completely
false to completely true, through partially false and partially true.
According
to Barbalho (2001), the representation of a fuzzy set is given by the ordered
pair X, μΑ (X).
· A = {(X, μΑ (X))  X € U};
· X is the variable being studied;
· μΑ (X) is a function which image
belongs to the interval [0, 1];
· "1" represents the
concept of total relevance;
· "0" is not relevant.
3.1.1.
Membership Function
Each
fuzzy set, A, is defined in terms of relevance to a universal set, X, for a
function called membership function, assigning each element a number x, A (x)
in the closed interval [0 , 1] that characterizes the degree of membership of x
in A. The membership function has the form: A: x [0, 1].
Shaw
(1999) states that a membership function is a function that assigns numeric
degrees of membership for discrete values of a variable in their universe of
discourse.
According
Barbalho (2001), any function that maps the domain U in the interval [0, 1] can
be used as membership function. In practice, however, the triangular and
trapezoidal forms (figure 4), the simplicity of representation, are the most
frequently used.

Figure
4: Relevance Functions
3.2.
Systems Based In Fuzzy Rules
Most
computer systems have their knowledge represented by rules that dictate how
they should act. This representation is used for a long time, such as an ITS
that has its bases (modules described in the previous section) formed through
rules.
Systems
using fuzzy logic are not different. Their behaviors are also dictated by
rules. However, the rules used by them are called fuzzy rules. The fuzzy rules
are characterized by a conditional expression of the form: IF < fuzzy
antecedent expression THEN < fuzzy consequentexpression.
According
to Barbalho (2001), the antecedent is formed by a single proposition or a
combination of propositions and describes conditions found by the rule. And the
consequent describes an action to be taken in the case of all of the foregoing
propositions to be answered. The combination of propositions is done through
the logical operators "AND" and "OR".
An
example: "IF a very drunk man and age less than 18 years THEN contact the
juvenile court." We demonstrated, by example, that the understanding of
some points is still needed:
· Linguistic variables versus
numerical values of the variables (age versus 18 years) are interpreted using
fuzzy logic.
· Linguistic variables intensity
(drunk can have a finite number of linguistic terms associated with it, they
can go from extremely drunk to not even drunk), can also be interpreted by
fuzzy logic.
· When the antecedents have
combinations of fuzzy propositions, or fuzzy rules, (associated with degrees of
membership), the degree of membership of the consequent depends on the
antecedent.
3.3.
Fuzzy Inference Systems
According
to Wagner (quoted in COSTA et al., 2003), fuzzy inference systems are based on
fuzzy inference rules using the fuzzy linguistic variables (fuzzy sets) to
perform a process of decisionmaking systems.
Fuzzy
inference systems are used to represent the interdependence between the
independent variables (inputs) and dependents (outputs) of a real system. The
basis of these systems is a set of fuzzy conditional rules, which must be
defined from the same set of assumptions (independent variables), with
responses belonging to the same domain (BÁRDOSSY cited by BARBALHO, 2001).
These
systems are generally based on a set of rules (knowledge base) type IFTHEN
describing the dependence between the linguistic inputs and outputs variables.
According
to Barbalho (2001), a fuzzy inference system is based on known values of the
input variables, and can make inferences about these data and obtain the values
of the output variables. In this case, the rules are inferred in parallel,
regardless of the order in which they are held. The interpretation or inference
of each rule consists of the evaluation of the foregoing propositions
(premises), after which the consequences. The following figure shows the
operation of the process.
Figure 5: Fuzzy
Inference System
3.3.1.
Fuzzyfication
Fuzzy
inference systems work with inaccurate information and / or vague terms of
natural language. However, when working with data entry computer systems, these
are usually numerical values given to the system.
For
example, a system that aims to monitor the conditions of a fuel storage tank
and take some action depending on them, using for that, data on temperature and
pressure. When data is sent to the system, they inform numerical values of
temperature and pressure.
Because
fuzzy systems work with linguistic terms, it is necessary to transform these
data into fuzzy sets. Therefore, a mapping is performed of the input data
(generally discrete numbers) on fuzzy numbers. It is the process of
fuzzyfication.
So
in this transformation, the numerical data values for each input variable are
modeled with membership functions associated with the corresponding variable,
and its resulting degree of membership of each value in the corresponding
linguistic terms (BARBALHO, 2001).
In
the above example, the value of 35 ° C temperature of the input variable to be
converted can be represented by the standard value cloudy and have a degree of
relevance, for example, 0.7, associated with it.
3.3.2.
Inference Process
The
process of inference, also called logical decisionmaking, is responsible for
evaluating the input variables by applying the rules of the knowledge base and
assigning responses to processing. It consists of three stages: Evaluation of
Assumptions; Implication; Aggregation and Consequences.
After
the fuzzyfication of input variables, the fuzzy rules are evaluated one by one
and calculate the degrees of relevance of each proposition. Each combination of
propositions (each rule) is applied to a function (the logical operator is used
depending on the combination of propositions) to produce a number between 0 and
1 that represents the degree to which the conditional expression of the rule is
satisfied (degree of applicability of the rule).
The
functions most commonly applied in this process are: the maximum function for
the operator "OR", and the function minimum, the operator
"AND". This step is the evaluation of assumptions.
According
to Barbalho (2001), the implication is used to calculate the consequences of
the rules which conditions are satisfied to some degree, based on their degree
of applicability. In cases where the rules have more than one result, all
consequences are equally affected by the degree of applicability.
When
the fuzzy inference system treats the input variables and verifies the rules,
generally, is more than one applicable rule. However, it is necessary to
generate a single response for each output variable. Aggregation Consequents
consists of aggregate, or combine, the consequences of those obtained by
inference rules (BARBALHO, 2001). Most often, this aggregation is done using
the function maximum which corresponds to the union of fuzzy sets.
3.3.3.
Defuzzyfication
After
the process of fuzzy inference, a fuzzy set answer is obtained, but often this
is good not enough for the system response, the system user has difficulties
for understanding it. A more appropriate numerical representation of a fuzzy
response is required. It is the deffuzzyfication process.
Taking
again the example of the system that monitors the fuel tank. At some point, the
fuzzy response must be transformed into a discrete number that represents the
activation of the alarm, for example.
Barbalho
(2001) presents the schemes of numerical representation of fuzzy sets most
commonly used:
· First of Maxima: selects the first
element among those that have the maximum degree of membership.
· Last of Maxima: selects the last
element among those that have the maximum degree of membership.
· Maximum Average: calculates the
average of the elements that has the maximum degree of membership.
· Centroid: choose the central
element (center of gravity) of the fuzzy set defined area.
4.
EDUCATIONAL
APPLICATIONS
Troubleshooting
as transmission of concepts and assessing learning is widely used. Therefore, a
tool like this could not fail to be present in intelligent tutoring systems.
For
an ITS to work with problem solving, it is important to adopt a database of
problems (solutions containing both the teachers and the solutions obtained by
the students). From these databases of problems, the system will need to
propose problems for the learner, based on the students’ level of expertise in
the subject matter covered, their preferences and level of difficulty of the
problem. It is also necessary that the system has mechanisms to assess problems
solved. These assignments fit to an agent (assistant troubleshooting) ITS.
This
agent, through communications with the tutor agent acquires the necessary
information about the student, such as knowledge level, personal preferences;
subject addressed, among others, and is better able to offer consistent
problems with the reality of the learner.
The
task of evaluating these issues is made using fuzzy logic. This, through
information and level of difficulty of the problem, knowledge level of the
student input variables and data of the problem, among others will be able to
infer a concept for the problem solved or even apply a grade.
5.
CONCLUSIONS
It
is almost unanimously asserted that a country is able to develop through investing
in education. It is therefore important to develop tools to help in the
educational process. Research in this area has grown significantly in recent
years. All contributions are important for the development of effective
education systems.
The
applications of fuzzy logic in the field of education are quite promising.
Integrating it with other techniques of artificial intelligence technologies is
making the traditional and distance learning increasingly adaptable to the
needs of students. This reality will increasingly allow for a quality education
which is studentcentered, and without borders.
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