PLANNING BY CASE-BASED REASONING BASED ON FUZZY LOGIC

Sundarapandian et al. (Eds) : CSE, CICS, DBDM, AIFL, SCOM - 2013
pp. 53–64, 2013. © CS & IT-CSCP 2013 DOI : 10.5121/csit.2013.3306
PLANNING BY CASE-BASED REASONING
BASED ON FUZZY LOGIC
Atmani Baghdad, Benbelkacem Sofia and Benamina Mohamed
Computer Science Laboratory of Oran (LIO)
Department of Computer Science, University of Oran, Algeria
BP 1524, El M’Naouer, Es Senia, 31 000 Oran, Algeria
{atmani.baghdad, sofia.benbelkacem, benamina.mohamed}@gmail.com
ABSTRACT
The treatment of complex systems often requires the manipulation of vague, imprecise and
uncertain information. Indeed, the human being is competent in handling of such systems in a
natural way. Instead of thinking in mathematical terms, humans describes the behavior of the
system by language proposals. In order to represent this type of information, Zadeh proposed to
model the mechanism of human thought by approximate reasoning based on linguistic
variables. He introduced the theory of fuzzy sets in 1965, which provides an interface between
language and digital worlds. In this paper, we propose a Boolean modeling of the fuzzy
reasoning that we baptized Fuzzy-BML and uses the characteristics of induction graph
classification. Fuzzy-BML is the process by which the retrieval phase of a CBR is modelled not
in the conventional form of mathematical equations, but in the form of a database with
membership functions of fuzzy rules.
KEYWORDS
Automatic Learning, Fuzzy Logic, Boolean Modelling, CBR, Induction graph.
1. INTRODUCTION
The problem of planning and scheduling of tasks is one of the most complex problems in the field
of Artificial Intelligence. The best-known situations include crisis management, production
management, project management, robotics, medical, etc. The goal of planning is to provide a
system (robotics, computer, human, ...) the capacity to reason to interact with its environment in
an autonomous manner, in order to achieve the objectives that have been assigned. Planning is
defined in terms of problems to be resolved and proposes a set of operators of change of State of
the world, given a representation of the initial state of the world, and a goal to be attained, to give
the means to a computer system to find a sequence of actions to be applied to the world to move
from the initial state to a State that satisfies the goal to achieve.
Scheduling is organized in time a set of tasks. Historically, scheduling problems were discussed
initially in the field of operational research (graph dynamic programming, linear programming,
methods of combinatorial optimization theory), but quickly showed their limits in terms of
expressiveness. Artificial intelligence and knowledge-based systems are then addressed the
problem, renewing techniques through a richer representation of the domain knowledge
(problems of satisfaction of constraints, constraints propagation algorithms, constraint
programming languages). Among knowledge-based systems we looked on the reasoning from
case (CBR).

54 Computer Science & Information Technology (CS & IT)
The CBR based on artificial intelligence techniques is an approach to problem solving that uses
past experiences to solve new problems by finding similar cases in its knowledge base and
adapting them to the particular case. All the experiences form a case basis. Each case is
represented by a knowledge experience. This experience is a lesson for the CBR system to solve
problems of various kinds. The CBR consists of five phases : 1-Elaboration of the case. 2-
Retrieval; 3-Adaptation; 4-Review and finally 5-Memory. For our project we are interested in the
second phase: retrieval.
Therefore our contribution in this area is double, on the one hand offer a reactive planning
module based on a CBR for the optimization of the scheduling, and on the other hand offer a
classification induction graph [10] for the acceleration of the indexing of cases : remembering.
The classification issue is to assign the various observations to categories or predefined classes
[16] [2]. In general classification methods consist in several stages. The most important step is to
develop the rules of classification from a priori knowledge; It is the learning phase [11].
The classification by inductive learning finds its originality in the fact that humans often use it to
resolve and to handle very complex situations in their lives daily [19]. However, the induction in
humans is often approximate rather than exact. Indeed, the human brain is able to handle
imprecise, vague, uncertain and incomplete information [18]. Also, the human brain is able to
learn and to operate in a context where uncertainty management is indispensable. In this paper,
we propose a Boolean model of fuzzy reasoning for indexing the sub-plans, based on
characteristics of the classification by inductive learning in humans [22].
This article is structured as follows. Section 2 presents a state of the art of work about planning
and data mining. Section 3 is devoted to the construction of the base of the case. In section 4 we
discuss classification by inductive learning from data and in particular the induction of rules by
graph of induction. In section 5 we introduce Boolean modeling [1]. Fuzzy logic is discussed in
section 6. Section 7 presents results of experimentation. Finally, we present the guidance of our
contribution and experimentation and we conclude in section 8.
2. STATE OF THE ART
We present previous work which have combined planning and data mining.
Kaufman and Michalski [15] propose an approach that involves the integration of various
processes of learning and inference in a system that automatically search for different data mining
tasks according to a high-level plan developed by a user. This plan is specified in a language of
knowledge production, called KGL (Knowledge Generation Language).
Kalousis and al. [14] propose a system that combines planning and metalearning to provide
support to users of a virtual laboratory data mining. The addition of meta-learning to planning
based data mining support will make the planner adaptive to changes in the data and capable of
improving its advice over time. Planner based on knowledge is based on ontology of data mining
workflow for planning knowledge discovery and determine the set of valid operator for each
stage of the workflow.
Záková and al. [20] have proposed a methodology that defines a formal conceptualization of the
types of knowledge and data mining algorithms as well as a planning algorithm that extracts the
constraints of this conceptualization according to the requirements given by the user. The task of
building automated workflow includes the following steps: converting the task of knowledge
discovery into a planning problem, plan generation using a planning algorithm, storing the
generated abstract workflow in form of semantic annotation, instantiating the abstract workflow
with specific configurations of the required algorithms and storing the generated workflow.

Computer Science & Information Technology (CS & IT) 55
Fernández and al. [12] presented a tool based on automated planning that helps users, not
necessarily experts on data minig, to perform data mining tasks. The starting point will be a
definition of the data mining task to be carried out and the output will be a set of plans. These
plans are executed with the data mining tool WEKA [19] to obtain a set of models and statistics.
First, the data mining tasks are described in PMML (Predictive Model Markup Language). Then,
from the PMML file a description of the planning problem is generated in PDDL (the standard
language in the planning community). Finally, the plan is being implemented in WEKA (Waikato
Environment for Knowledge Analysis).
3. CONSTRUCTION OF THE CASE BASE
Case-based reasoning is one of the currently most widely used artificial intelligence techniques.
Reasoning from cases is to solve a new problem, called problem target, using a set of problems
already solved. A source case refers to an episode from problem solving and a case one basis
together cases sources [3]. A case consists of two parts: the problem and the solution part. The
problem part is described by a set of indices that determine in what situation a case is applicable.
Case-based reasoning process generally operates under five sequential phases: development,
remembering (or indexing), adaptation, the revision and learning.
Scheduling based on the case is a planning approach that is based on a particular aspect of human
behaviour. Generally, the man does not generate plans (calendar) entirely new from basic
operations; he uses his experiences (success or failure) to help solve new problems that arise to
him. Establish a schedule returned to try to synthesize a solution plan, by reusing the best plans
already produced in similar situations and changing to adapt to the new situation. Planning from
case, a scheduling problem is the specification of an initial state and a goal to achieve. A solution
is a plan for achieving the purpose starting from the initial state.
For a system of case-based reasoning to work, it must start from a certain number of cases
constituting the basis of cases. These cases should cover the target area the best possible so
interesting solutions are found. Take the example of the treatment of a disease reportable:
tuberculosis. The treatment of tuberculosis differs depending on the patient's age and various
other factors. We are building the basis of cases passing through four steps: the project
description, modeling of the project by a graph or, the generation of the plans, the construction
and representation of cases [6].
The description of the project is to represent the sequence of tasks or actions as an array.
Then, a graph or is generated from the project. The graph is a graph whose nodes represent tasks
or arcs represent the relationships between tasks. The relationship between the tasks being to
satisfy constraints [4]. Constraints are criteria that may be taken into account in the development
of sub-plans. The choice of a solution plan depends on several criteria: time, probability, and the
cost. However a task represents the action carried out for a period of time [17].
After the construction of the graph, we and/or apply planning algorithms to determine the
possible plans. The scheduling algorithm we use is based on a course of the graph or back
chaining. It is to find possible paths between the initial node and the final node of the graph
and/or. The algorithm stops when the sought initial node is found [8].
To build the case, we will link a duration, a probability and a cost to each plan obtained in the
previous step according to its tasks. Therefore cases will be represented by descriptors (duration,
cost, likelihood) that describe the problem part and the corresponding plane that represents the
solution part. Table 1 presents the basis of 14 cases.

4. CLASSIFICATION OF PLANS BY INDUCTIVE LEARNING
Establish a plan, means being able to associate the subplan to a number of indices presented by
situations. In this type of problem, it identifies three essentials: problems, plans and indices.
Problems are the population, indices are the descriptions of the problems and plans are the
classes. It is assumed that there is a correct classification, meaning that there is an application that
associates any scheduling problem with a plan. Learn how to develop a plan, is to associate a plan
already drawn up a list of indices. To formalize this connection, we will use the following
notations: = {w1,w2,...,wn} to refer to a population of n scheduling problems. G={g1,g2,...,gd}
for all d descriptions (indices of the problem) and Q={q1,q2,...,qm} for all the plans m .
Is a population of individuals affected by the problem of classification. This population is a
special attribute called noted class attribute is associated. The variable Y is called the area of
variable statistics endogenous or simply class. At each individual w may be associated with its
class Y(w). They say that the function is takes its values in the set of labels Q, called also whole
classes. For example, if the population is diabetic patients and is the result of the identification
of diabetes type 1 noted q1, and type 2 noted q2; then Y(w) will be the result of the identification
of the type of diabetes the patient w [1].
The determination of the classification model ϕ is related to the assumption that the values taken
by the variable Y are not random, but certain specific situations that can characterize [22]. For this
the expert in the field concerned establishes a priori list of p variable statistical called variables
exogenous and rated X= {X1,X2,...,Xp}. These variables are also called predictive attributes or
explanatory. The value taken by a variable exogenous Xj is called modality or value of attribute Xj
of the problem w. We mean by lj the number of terms that a variable Xj can receive. To illustrate
this notation, consider the problem of planning. A problem can be described, for example, by
three exogenous variables:
X1: Duration, which can take three values 1
1x =Courte, 2
1x =Normale, 3
1x =Longue
X2: Probability, which can take three values 1
2x =Incertain, 2
2x =Douteux, 3
2x =Certain
X3: Cost, which can take three values 1
3x =Faible, 2
3x =Raisonnable, 3
3x =Elevé
Inductive learning aims to seek a classification model ϕ allowing for a new case w, for which we
do not know the class Y (w) but we know the State of all of its variables exogenous to predict this
value throughj. The development of ϕ requires in the population two samples graded A and
T. The first said of learning will be used for construction and the second said to test will be used
to test the validity of ϕ. Thus, for any case w, we assume known both its values X (w) in the space
of representation and its class Y (w) space labels Q.
Population A cases, taken into account for classification is nothing more than a sequence of n
case w i (situations) with their plan corresponding Y(wi). Suppose that the A sample is composed
of 14 situations (table 1):

Table 1. Example of a learning sample.
Supervised inductive learning intends to provide tools for extracting the classification model
based on the information available on the sample of learning ϕ. The general process of inductive
learning includes typically three steps that we summarize below:
1. Development of the model: This is the step that uses a sample of noted learning A , which
all individuals wi are described in a space of representation and belong to one of the m
classes denoted cj, j= 1,...,m. It is building the application ϕ which allows calculating the
class from representation.
2 Validation of the model: This is to verify on a sample test T and which we know for each of
its individuals, representation and the class, if the classification model ϕ from step previous
gives of the class expected.
3 Generalization of the model: This is the stage which is to extend the application of the model
to all individuals of the population .
5. BOOLEAN MODELING OF THE INDUCTION GRAPH
In this section, we present the principles of construction, by Boolean modelling [1,5,9,23,24], of
induction graphs in the problems of discrimination and classification [1,2] : we want to explain
the class taken by one variable to predict categorical Y, attribute class or endogenous variable;
from a series of variables X1, X2,..., Xp, say variable predictive (descriptors) or exogenous, discrete
or continuous. According to the terminology of machine learning, we are therefore in the context
of supervised learning. The general process of learning than the cellular system CASI (Cellular
Automata for Symbolic Induction) [1] applies to a population is organized on three stages:
1) Boolean modeling of the induction graph;
2) Generation of the rules for cases indexing;
3) Validation and generalization;
Ω Y(ω) X1(ω) X2(ω) X3(ω) Ω Y(ω) X1(ω) X2(ω) X3(ω)
ω1 Plan1 75 0,70 70 ω8 Plan1 64 0,40 65
ω2 Plan2 80 0,80 90 ω9 Plan1 65 0,80 75
ω3 Plan2 85 0,85 85 ω10 Plan2 51 0,10 80
ω4 Plan2 72 0,20 95 ω11 Plan2 55 0,50 70
ω5 Plan1 79 0,69 70 ω12 Plan1 49 0,52 80
ω6 Plan1 71 0,70 90 ω13 Plan1 58 0,81 80
ω7 Plan1 63 0,30 78 ω14 Plan1 40 0,90 96

Figure 1 summarizes the general diagram of the Boolean modeling process in the CASI system.
Figure 1. General diagram of the system CASI
From the sample A we begin the symbolic treatment for the construction of the induction graph
(method SIPINA [21] [22].
1) Choose the extent of uncertainty (Shannon or quadratic);
2) Initialize the parameters λ, µ and the initial partition S0 ;
3) Use the SIPINA method to pass partition St to St + 1 and generate the graph of induction.
4) Finally, generation of prediction rules.
Method SIPINA [21] algorithm is a non tree heuristic for the construction of a graph of induction.
Its principle is to generate a succession of scores by merger or breakup of the nodes of the graph.
In what follows we describe the process on the fictional example of table 1. Suppose our sample
of learning A consists of 14 cases of scheduling which are divided into two classes plan1 - plan2
(see table 1). The initial partition S0 has one s0noted element, which includes the entire sample
learning with 9 situations belonging to the class plan1 and 5, class plan2. The next partition S1 is
generated by the variable X1 after discretization and individuals in each node si are defined as
follows: s1={ω∈ A|X1(ω)=Longue pour X1(ω) >=72}, s2={ω∈ A|X1(ω)=Normale pour X1(ω)
>=60 et X1(ω)<72} and s3={ω∈ A|X1(ω)=Courte pour X1(ω) <60}.
As well as in the s0 node, there are in s1, s2 and s3, individuals of the plan1 and plan2classes. The
figure 2 summarizes the steps of construction of s0, s1, s2 and s3. The S1partition, the process is
repeated looking for a S2 score which would be better.
Figure 2. Construction of the nodes s0, s1, s2 and s3
To illustrate the architecture and the operating principle of the BIG module, we consider figure 2
with the S0= (s0) partitions and S1= (s1,s2,s3). Figure 3 shows how the knowledge extracted from
SIPINA
Symbolic
Learning
BOG
Boolean
Opt & Gen
BIG
Boolean
Inferenc
Engine
BVG
Boolean
validation
Boolean KB
CASI
User interfaceΩA ΩT ΩE
Partition S0
X1
Plan1
Plan2
9
5
s0
Courte
3
2
s3
Norm
ale
4
0
s2
Longue
2
3
s1Partition S1

RE ARC1 ARC2 ARC3
s0 1 1 1
X1=longue 0 0 0
s1 0 0 0
X1=normale 0 0 0
s2 0 0 0
X1=courte 0 0 0
s3 0 0 0
RS ARC1 ARC2 ARC3
s0 0 0 0
X1=longue 1 0 0
s1 1 0 0
X1=normale 0 1 0
s2 0 1 0
X1=courte 0 0 1
s3 0 0 1
this graph database is represented by the CELFACT and CELRULE layers. Initially, all entries in
cells in the CELFACT layer are passive (E= 0), except for those who represent the initial basis of
facts (E= 1).
Figure 3. Boolean partitions modeling S0 and S1
In figure 4 are, respectively, represented the impact of input matrices RE and exit RS the Boolean
model.
· the relationship entry, denoted i RE j, is formulated as follows:∀i∈{1,..., l},∀j∈{1,..., r}, if (the
fact i ∈ to the premise of the j rule) then RE(i, j) ← 1.
· the relationship of output, denoted i RS j, is formulated as follows:∀i∈{1,..l}, ∀ j∈ {1,..., r}, if
(the fact i ∈ the conclusion of rule j) then RS(i, j) ← 1.
Figure 4. Input/output incidences matrices
Incidence matrices RE and RS represent the relationship input/output of the facts and are used
in forward-chaining [1] [9]. You can also use RS as relationship of input and RE as relationship of
output to run a rear chaining inference. Note that no cells in the vicinity of a cell that belongs to
CELFACT (at CELRULE) does not belong to the layer CELFACT (at CELRULE).
The dynamics of the cellular automaton BIG [1,23], to simulate the operation of an Inference
engine uses two functions of transitions δfact and δrule, where δfact corresponds to the phase of
assessment, selection and filtering, and δrule corresponds to the execution phase [1,24]. To set the
two functions of transition we will adopt the following notation: EF, IF and SF to designate
CELFACT_E, _I and _S; Respectively ER, IR and SR to designate CELRULE_E, _I and _S.
-The transition function δfact: (EF, IF, SF, ER, IR, SR) (EF, IF, EF, ER+(RE
T
·EF), IR, SR)
-The transition function δrule : (EF, IF, SF, ER, IR, SR) (EF+(RS·ER), IF, SF, ER, IR, §ER)
Where RE
T
matrix is the transpose of RE and where §ER is the logical negation of ER. Operators +
and · used are respectively the or and the and logical.
We consider G0 initial configuration of our cellular automaton (see figure 4), and ∆ = δrule ο δfact
the global transition function: ∆ (G0) = G1 if δfact (G0) = G'0 and δrule (G'0) = G1. Suppose that
CELFACT E I S
s0 1 1 0
X1=longue 0 1 0
s1 0 1 0
X1=normale 0 1 0
s2 0 1 0
X1=courte 0 1 0
s3 0 1 0
CELRULE E I S
ARC1 0 1 0
ARC2 0 1 0
ARC3 0 1 0
ARC1 : Si s0 Alors (X1=longue) et s1.
ARC2 : Si s0 Alors (X1=normale) et s2.
ARC3 : Si s0 Alors (X1=courte) et s3.

G = {G0, G1,..., Gq} is the set of Boolean PLC configurations. Discrete developments plc, from
one generation to another, is defined by the sequence G0, G1,..., Gq, where Gi+1=∆(Gi)
[1,23,24].
6. FUZZY BOOLEAN MODELING
According to Lotfi Zadeh [19], founder of fuzzy logic, the limits of the classical theories applied
in artificial intelligence come because they require and manipulate only accurate information.
Fuzzy logic provides approximate reasoning modes rather than accurate. It is mainly the mode of
reasoning used in most cases in humans.
According to Zadeh, fuzzy logic is fuzzy sets theory which is a mathematical theory, whose main
objective is the modeling of the vague and uncertain of the natural language concepts. Thus, it
avoids the inadequacies of the traditional theory regarding the treatment of this kind of
knowledge. The fundamental characteristic of a classic set is rigid boundary between two classes
of elements: those who belong to all and those who do not belong to this set. they belong rather to
its complement. The relationship of belonging is represented in this case by a µ function that
takes truth values {0,1} pair. Thus, the membership of a classic set A function is defined by:



∉
∈
=
Axif
Aif
xA
0
x1
)(µ
This means that an element x in A (µA(x)=1) or not (µA(x)=0). However, in many situations, it is
sometimes ambiguous whether x belongs or not to A.
As an example for the definition of the membership functions, it takes the variable X3 = Coût of
table 2. According to the (logical Boolean) classical logic, which allows for variables that two
values 0 and 1, all costs less than 40 are considered low, and those over 70 as high. However such
logic of classification does not make sense. Why a cost of 75 is considered higher? in reality such
a passage is done gradually. Fuzzy logic variables may take any values between 0 and 1 to take
account of this reality.
In the simplest case, one can distinguish three values Faible, Raisonnable, and Elevé, of the
language variable “Coût” which forms three fuzzy sets (figure 5). Thus, a cost of 35 belongs with
a factor of belonging µ = 0.75 across ' Faible' and with µ = 0.25 to all 'Raisonnable'. Obviously,
the choice characterizing the trapezoidal shape of the membership function is quite arbitrary and
must take account of the particular circumstances. Often, it is necessary to introduce a subdivision
more fine, e.g. 5 values «très faible», «faible», «raisonnable», «élevé» and «très élevé» for the
language variable 'Cost', thus forming 5 sets. Thus a cost of 35 belongs, with µ = 0.25, across '
faible '.

Figure 5. Classification of the cost according to the logic fuzzy
Suppose now that from the induction graph obtained with the method SIPINA we generated five
rules R1, R2, R3, R4 and R5 of classification that we'll use for the indexing of cases. The following
illustration shows the Boolean modelling of extracted knowledge base.
Figure 6. Boolean modelling of extracted knowledge base
40 70
35
0,75
0,25
µ
x
Faible Raisonnable Elevé
30
80
40 70
35
µ
x
Faible Raisonnable Elevé
R1 : Si (X1=Longue) et (X3=Faible) Alors plan1.
R2 : Si (X1=Longue) et (X3=Elevé) Alors plan2.
R3 : Si (X1=Normale) Alors plan1.
R4 : Si (X1=Courte) et (X2=Incertain) Alors plan2.
R5 : Si (X1=Courte) et (X2=Douteux) Alors plan1.
RE R1 R2 R3 R4 R5
X1=Longue 1 1 0 0 0
X1=Normale 0 0 1 0 0
X1=Courte 0 0 0 1 1
X2=Incertain 0 0 0 1 0
X2=Douteux 0 0 0 0 1
X2=Certain 0 0 0 0 0
X3=Faible 1 0 0 0 0
X3=Raisonnable 0 0 0 0 0
X3=Elevé 0 1 0 0 0
Plan1 0 0 0 0 0
Plan2 0 0 0 0 0
RE R1 R2 R3 R4 R5
X1=Longue 0 0 0 0 0
X1=Normale 0 0 0 0 0
X1=Courte 0 0 0 0 0
X2=Incertain 0 0 0 0 0
X2=Douteux 0 0 0 0 0
X2=Certain 0 0 0 0 0
X3=Faible 0 0 0 0 0
X3=Raisonnable 0 0 0 0 0
X3=Elevé 0 0 0 0 0
Plan1 1 0 1 0 1
Plan2 0 1 0 1 0
CELFACT E I S
X1=Longue 1 1 0
X1=Normale 0 1 0
X1=Courte 0 1 0
X2=Incertain 0 1 0
X2=Douteux 0 1 0
X2=Certain 0 1 0
X3=Faible 0 1 0
X3=Raisonnable 0 1 0
X3=Elevé 0 1 0
Plan1 0 1 0
Plan2 0 1 0
CELRULE E I S
R1 0 1 0
R2 0 1 0
R3 0 1 0
R4 0 1 0
R5 0 1 0

6.1. Boolean Fuzzification of Exogenous Variables
Fuzzy-BML modelling deals with the fuzzy input variables and provides results on output
variables themselves blurred. Fuzzification, illustrated by the following example, is the step that
consists of fuzzy quantification of actual values of a language variable.
Fuzzifier to: the universe of discourse, i.e. a range of possible variations of the corresponding
entry. A partition interval fuzzy from this universe, for the identification of the cost we
partitioned space of X3 to 7 with a Boolean modeling on 3 bits of 000 to 110. Finally, the duties
of membership classes.
6.2. Boolean Defuzzification
Output the Fuzzy-BML modeling cannot communicate to the user of the fuzzy values. The role of
the defuzzification is therefore to provide accurate values. During this step, the system will
perform tests to define the range of proven goal. This test will depend on the number of rules
candidates and the de facto number of each rule that participated in the inference according to the
following principle:
• Cases for a single rule and a single fact: "if then conclusion.
CELFACT _I (conclusion) = minimum (CELFACT_I (fact), CELRULE(rule) _I).
• Cases for a single rule with several facts: ' If fait1 and fait2 and... .' then conclusion» :
CELFACT_I (conclusion) = minimum (CELFACT_I (fait1), CELFACT(fait2) _I, ...).
The 'minimum' operator in Boolean logic represents the "and logical."
• Several rules:
CELFACT _I (goal) = maximum (CELRULE_I (rule1), CELRULE_I (rule2),...).
The 'maximum' operator in Boolean logic represents the "logical or". Figure 7 shows the Boolean
principle adopted by the Fuzzy-BML modeling.
Figure 7. Boolean for the defuzzification operator
Interface de fuzzification
Coût faible à 25%
Coût faible à 75%
Coût faible à 100%
X3 = 42

7. EXPERIMENTATION
We have evaluated our approach on a case basis about the treatment of tuberculosis. The case
basis contains actual cases collected from the CHU of Oran [7]. The problem part of cases is
described by three descriptors given in Table 2 and the solution part is given in the form of a
treatment plan Y which takes its values in the set of plans C={T1, T2, T3, T4}.
Table 2. Values of descriptors.
Descriptors Meaning Values
X1 Age < 20, 20-30, 30-40, 40-50, >50
X2 Weight 30-39, 39-54, 54-70, >70
X3 Antecedent NT, T
To compare the proposed approach with other methods, we have applied the k-NN [13], the
decision tree and the Fuzzy-BML on the same case base. We show in Table 3 the rate of correctly
classified instances with each method using the supervised mode of discretization.
Table 3. Results of experimentation.
k-NN Decision tree Fuzzy-BML
66 % 73 % 81 %
The rate of correctly classified instances is 66 % with k-NN, 73 % with decision tree and 81 %
with Fuzzy-BML. From the obtained results, we note that the Fuzzy-BML method has provided
better results with a rate of 81 % of well classified instances.
8. CONCLUSIONS AND PERSPECTIVES
Several competing motivations have led us to define a Boolean model for CBR knowledge base
systems. Indeed, we have not only desired experiment with a new approach to indexing of cases
by decision tree, but we also wanted improve modeling of the vague and uncertain of the natural
language concepts. When it comes to planning guided by CBR, we must go through the following
steps:
- Build the base of cases by planning tools;
- Construct the graph of induction by symbolic learning and extract the rules;
- Import knowledge base in the platform WCSS [5].
- Launch the Boolean fuzzification [9] ;
- Launch the inference blurred for indexing in the basis of the cases;
- Finally, and if necessary run the Boolean defuzzification.
For the calculation of the similarity in the retrieval (cases indexing) phase, typically used k-
nearest neighbours. So we compared our Fuzzy Boolean Model with k-nearest neighbours (k-NN)
and decision tree. We noticed that the indexing of cases for the choice of a plan is significantly
better with Fuzzy-BML. Finally, we can say that the structure of the cases that we have used is
quite simple. We have described the part problem of cases by age, weight and a antecedent. By
adding other constraints could subsequently used a slightly more complex representation. As a
future perspective of this work, we propose to improve the other steps of the CBR process for the
proposed approach

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