Informatica 40 (2016) 237–244 237
FuAGGE: A Novel System to Automatically Generate Fuzzy Rule Based
Learners
Romaissaa Mazouni and Abdellatif Rahmoun
Djilali Liabes University, Computer Science Departement, Algeria
E-mail: rom.mazouni@yahoo.com
Eric Hervet
Moncton University, Computer Science Departement, NB, Canada
Keywords: FuAGGE, grammatical evolution, fuzzy set covering, fuzzy rule-based learners, data mining
Received: January 6, 2016
Data in real world applications are in most cases linguistic information that are ambiguous and uncertain.
Hence, such data should be handled by fuzzy set representation schemes to increase expressiveness and
comprehensiveness. Moreover, mining these data requires ways to generate automatically useful infor-
mation/knowledge through a set of fuzzy rules. This paper proposes a novel system called FuAGGE that
stands for Fuzzy Automatic Generator Genetic Expression. The FuAGGE approach uses a grammar based
evolutionary technique. The grammar is expressed in the Backus Naur Form (BNF) and represents a fuzzy
set covering method. The grammar is mapped into programs that are themselves implementations of fuzzy
rule-based learners. Binary strings are used as inputs to the mapper along with the BNF grammar. These
binary strings represent possible potential solutions resulting from the initializer component and the build-
ing blocks from Weka, a workbench that contains a collection of visualization tools and algorithms for data
analysis and predictive modeling. This operation facilitates the induction process and makes induced pro-
grams shorter. FuAGGE has been tested on a benchmark of well-known datasets and experimental results
prove the efficiency of the proposed method. It is shown through comparison that our method outperforms
most recent and similar, manual techniques. The system is able to generate rule-based learners specialized
to specific domains, for example medical or biological data. The generated learners will be able to pro-
duces efficient rule models. The produced rule models will achieves more accurate classification for the
specific used domain.
Povzetek: Razvit in testiran je algoritem FuAGGE za učenje mehkih pravil, ki omogoča učenje s slovnico,
prilagojeno vsaki problemski domeni.
1 Introduction
Fuzzy systems have gained popularity due to their ability
to express ambiguous and uncertain information in various
real-world applications [1, 2, 3]. Hence, in order to take
advantage of the well-established foundations of predicate
logic-based expert systems, researchers focus on extract-
ing fuzzy knowledge from available numerical data [4].
Yet, in [5], the authors propose a fuzzy extension of a rule
learner called FILSMR, where they apply fuzzy set con-
cepts [6] to the algorithm PRISM [7]. Later on, Wang and
al proposed an algorithm called Fuzzy-AQR [8], where
they introduced a seed that represents the highest member-
ship to the positive set. It is used to generate an initial rule
which should cover the seed. In [9], Van Zyl and al pro-
pose FuzzConRi. It is mainly based on the CN2 method
[10]. FuzzConRi is composed of two layers: The upper
layer uses a set covering approach, while the lower one is
used to induce a single rule. Later on, in [11, 12], the
same previous authors propose the Fuzzy-BEXA frame-
work. This framework consists of three layers: The top
layer implements a set covering approach, the middle layer
uses heuristics to guide the search, and the lower layer is
dedicated to refining conjunctions. Huhn and al introduced
a new rule learner called FURIA [13]. This is a fuzzy ex-
tension of the RIPPER algorithm [14], except the fact that
it learns fuzzy unordered rule sets instead of conventional
rule lists. It also uses a rule stretching method to solve the
problem of uncovered records. In 2014 Swathi et al [15]
used fuzzy classification entropy to generate fuzzy deci-
sion tree (FDT) and later the parameters of FDT are tuned
to further increase the accuracy of FDT. Nevertheless, all
of existing methods in the current literature rely on design-
ing fuzzy rule learners manually .In this work we present
a grammar evolution based system that automatically gen-
erates such rules. We believe that automating the process
of writing fuzzy rule based classifiers can highly improve
the efficiency of such classifiers. Yet, an automatic genera-
tion of fuzzy rule based classifiers alleviates the burden of
writing long source codes. The proposed system relies on a
grammar that represents the overall structure for fuzzy set
covering approaches.
238 Informatica 40 (2016) 237–244 R. Mazouni et al.
The paper is composed of six sections in addition to the
above introduction: Section 2 describes the Grammatical
Evolution method. Section 3 describes the fuzzy rule-based
classifiers and their features. Section 4 illustrates the auto-
matic generation of fuzzy rule learners. Section 5 offers a
description of how the system automatically generates rule-
based learners. Section 6 presents the results obtained with
the proposed system, and finally section 7 concludes the
paper.
2 Grammatical evolution
Grammatical Evolution is a special case of grammar-based
genetic programming that uses a mapping procedure be-
tween the genotypes and the phenotypes of individuals
[16]. Grammatical evolution can generate complete pro-
grams in an arbitrary programming language using popu-
lations of variable-length binary strings. These computer
programs are solutions to a given problem [17, 18]. When
using Grammatical Evolution to generate solutions to a
given problem, there is no need to pay attention to the
genetic operators and how they are implemented: Gram-
matical Evolution ensures the validity of the generated pro-
grams for free. As described in [19], Grammatical Evolu-
tion applies concepts from molecular biology to the repre-
sentational power of formal grammars [20]. The genotype-
phenotype mapping in Grammatical Evolution has the ad-
vantage, over solution trees used in traditional Genetic Pro-
gramming, to allow operators to act on genotypes. By anal-
ogy to biological DNA, a string of integers that represents
a genotype is called a chromosome, and the integers that
compose a chromosome are called codons. A Backus Naur
Form grammar definition must be introduced prior to us-
ing Grammatical Evolution to solve a given problem. This
grammar describes the output language produced by the
system in [21, 22], and is used along with the chromo-
somes in the mapping process, which consists of mapping
non-terminals to terminals, and completed through convert-
ing the binary string data structure into a string of integers,
which is finally passed from the genetic algorithm on to
the Grammatical Evolution system. The string of integers
then goes through a translation process, where rules of the
BNF grammar are selected. The production rules, which
can be considered equivalent to amino acids in genetics, are
combined to produce terminals, which are the components
making up the final program. One problem that can oc-
cur when mapping binary strings is the production of short
genes, meaning we run out of genes, but there are still some
non-terminals to map. A solution to this issue is to wrap out
the individuals, and to reuse the genes. A gene can be used
several times in the mapping process. It is also possible
to declare some individuals as invalid by penalizing them
with a suitable harsh fitness value. The rules selection is
performed by using the mod ulo operator, and every time a
codon (an integer) is read, it is divided by the number of the
rule’s choices. The remainder of this division is the num-
ber of the rule to be selected. Grammatical Evolution can
be used to automatically generate fuzzy classifiers by us-
ing a grammar that represents the overall structure of these
fuzzy classifiers. The initial population which is a group of
individuals (integer arrays) is used along with the grammar
in the mapping process. The GE Mapper produces pheno-
types (fuzzy classifiers) which are evaluated using the fit-
ness function. Phenotypes go through an evolution process
in the Search Engine until a stopping criterion is met and a
best fit fuzzy classifier is found. The different modules of
the whole Grammatical Evolution approach are illustrated
in Fig. 1.
3 Fuzzy rule induction
One of the main and most studied tasks of data mining is
classification, which aims at predicting to which class be-
longs a certain element according to any given classifica-
tion model. The classification model can be a set of deci-
sion rules extracted, using a given dataset, and which rep-
resents local patterns of a model in this dataset. Decision
rules can be extracted from other knowledge representa-
tions such as Decision Trees [23]. Moreover, they can be
drawn out directly from the training set, or may also be in-
duced by using evolutionary algorithms, more specifically,
genetic algorithms or genetic programming. Fuzzy set the-
ory lead researchers to look for fuzzy alternatives for data
mining problems such as fuzzy induction learners, fuzzy
decision trees, and fuzzy clustering. The present work fo-
cuses on the sequential covering rule induction paradigm.
The fuzzy version of the sequential covering paradigm is
called fuzzy set covering. The proposed idea is to train one
rule at a time, remove the examples it covers, and repeat
the process until all data is fully covered, as described in
[24]. There are plenty of proposed algorithms that follow
the fuzzy set covering paradigm. These algorithms usu-
ally differ in some components such as the search mech-
anisms [25]. There are three different search strategies:
The bottom-up one starts with a random sample from the
dataset, then generalizes it; The top-down strategy starts
with an empty rule, then specializes it by adding precon-
ditions to it; Finally the bidirectional strategy, which is the
least common one, allows to either generalize or specialize
the candidates. There are also two different categories of
search methods. The most used ones are the greedy method
(ex: FILSMR [7]) and the beam method (ex: FuzzConRi
[9], FuzzyBEXA [12]). Covering algorithms have differ-
ent ways to evaluate rules. Some of the existing meth-
ods are: The fuzzy entropy (ex: fuzzy ID3 [26]), the
Laplace estimation (ex: Fuzzy- BEXA [12], FuzzConRi
[9]), the Fuzzy Bexa framework (fuzzy purity, the fuzzy
ls-content and fuzzy accuracy function), and the fuzzy info
gain (ex: FILSMR [6], Fuzzy-AQR [8]). The final compo-
nent that differentiates covering algorithms is the pruning
method, which consists in handling over fitting and noisy
data. There are two types of pruning: pre-pruning that deals
FuAGGE: A Novel System to Automatically. . . Informatica 40 (2016) 237–244 239
Figure 1: Grammatical Evolution Modules
with over fitting and noisy data, and post-pruning that deals
with rejection and conflicts in order to find a complete con-
sistent rule set. Pre-pruning offers the ability to obtain a
high-speed model, while post-pruning helps getting sim-
pler and more accurate models. The grammar we use is a
context-free grammar in Backus Naur form that contains
all elements necessary to build a basic fuzzy rule learner,
following the fuzzy set covering paradigm. It contains 19
production rules, each one representing non-terminal sym-
bols, and 40 terminal symbols describing the elements. The
grammar produces fuzzy rule set without any specific order
needed when applying them. This process provides differ-
ent initialization, refinement, and evaluation techniques.
4 Automatic generation of fuzzy rule
learners
To build a system that is able to generate fuzzy rule-based
learners, we used a context-free grammar that represents
the whole structure of the sequential fuzzy set covering
paradigm (Fig. 2). This grammar was built after review-
ing different fuzzy rule set inducers in the existing liter-
ature. It contains 19 rules and 40 terminals, where each
terminal stands for a building block performing an action.
Algorithm 1 illustrates the building block represented by
the terminal Include1Selector in the rule number 11 in the
grammar. It is worth mentioning that this method is the first
one quoted in the literature that automatically generates a
fuzzy rule induction algorithm. To do this, we put in place
a grammar evolution scheme. The decision rules model has
been selected on the basis of intuitiveness and comprehen-
siveness. In the following section, we propose a system
that combines Grammatical Evolution with a context-free
grammar, in order to generate code fragments possessing
the ability to generate accurate, noise-tolerant, and com-
pact decision fuzzy rule sets.
Algorithm 5 Include1Selector (rule R).
1: refinements = ∅
2: for i = 0 to i < numberAtt do
3: for for j = 0 to j < numberVal(Atti) do
4: newAntecedant = R U (Atti,V alj)
5: refinements = refinements U newAntecedant
6: end for
7: end for
8: return refinements
4.1 Proposed system: FuAGGE
The suggested method includes five main components. To
start, all what we need is a grammar that represents the
overall structure of all manually designed fuzzy rule learn-
ers that obeys to the fuzzy set covering technique. We use
some building blocks from Weka, which is a workbench
that contains a set of visualization tools and a set of algo-
rithms for data analysis and predictive modeling. This step
will help reading the dataset files, and testing the newly
generated rule based learners. It might be seen as "code
reusing". We also need some machine learning datasets in
order to train and test the newly generated learners. The
datasets we used were taken from the UCI machine learn-
ing repository [27]. Indeed, we need several and various
datasets, so that when fuzzy rule learners (candidate solu-
tions) are trained, these are not tailored to a specific do-
main. Finally, we have to take care of the mapper of the
Grammatical Evolution [17], modified in such a way that
when it reads terminals, pieces of Java code representing
these terminals actions are generated. At this stage, we
used the GEVA framework to implement the whole sys-
tem [18]. The most important component of our system
is the mapper, which must have the ability to read the in-
teger values from the chromosomes / candidate solutions
that are called in this paper the FuAGGE classifiers. Then,
we had to choose the appropriate corresponding rule to
240 Informatica 40 (2016) 237–244 R. Mazouni et al.
a given non-terminal, import some of the already coded
Weka building blocks, and insert them along with the ter-
minals corresponding to Java code into the Java class that
builds the new FuAGGE classifier. Fig. 2 represents the
whole system and its modules. Individuals in this system
are represented as integer arrays that are to be mapped to
the fuzzy rule learners. Every array is read one integer at
a time [28], and every integer is divided by the number
of choices of the current rule. The number of the rule to
be chosen and applied next is the remainder of the division
(Eq. 1), where N is the currently read integer, Nc is the
number of choices of the next rule to apply, and Idrule is
the identifier of the rule selected by the mapper. This rule
will be mapped into Java code (Fig. 3).
N mod Nc = Idrule (1)
When using Grammatical Evolution to solve a given
problem, we need a measure that favors the selection of the
best individuals among a population of possible solutions.
The metric, also called the fitness function, used in this
work to evaluate the FuAGGE classifiers generated during
the evolution process, is the accuracy method. After the
initialization of the first population, individuals go through
the mapping process and are integrated into Java programs
(FuAGGE classifiers), which are the actual classifiers that
need to be compiled and executed (trained and tested) using
different datasets. Each fuzzy rule learner has a set of dif-
ferent accuracies accuracy per dataset). The average of all
these accuracies is used as the classifiers overall accuracy,
so we are able to compare the different FuAGGE classifiers
over a population. The following equation defines the over-
all accuracy of a FuAGGE classifier in a given population.
acci;j represents the accuracy of the FuAGGE classifier i
using the dataset j, and h is the number of datasets:
f(i) =
h∑
j=0
accij
h
(2)
When using Grammatical Evolution, we do not need
to check the off-springs generated after a mutation or a
crossover operation, because the genetic operators are ap-
plied on genotypes: Since these are represented by integer
arrays, a crossover or a mutation operation over them gen-
erates the same type of arrays, which are then mapped us-
ing the grammar. This might not be always the case if we
were using the Context Free Grammar Genetic Program-
ming method, because the genetic operators are applied on
the phenotypes (syntax trees), and this may generate un-
suitable off-springs.
5 Experimental results and
discussion
Three components are needed so that the system can start
the evolution process: The grammar introduced in section.
4, the meta datasets, and finally the Grammatical Evolu-
tion parameters. The parameters have been set as follows:
the number of generation has been set to 60, the population
size to 150, the mutation probability to 1%, the crossover
probability to 80%, and the selection method is the tourna-
ment selection with generational replacement. We should
note here that all these parameters have been fixed empiri-
cally after that we analyzed a certain number of trials and
experimentations.
In order to evaluate the newly generated fuzzy learn-
ers, we computed the accuracies of two manually designed
fuzzy rule learners using all ten datasets. The last col-
umn of Table 1 reports accuracies of the new generated
fuzzy learners (FuAGGE classifier), while the remaining
columns shows the accuracies of the two manually de-
signed classifiers (Furia, Fuzzy CN2). The upper six rows
reports the accuracies of the fuzzy rules sets generated by
the FuAGGE-classifier, and the two baseline ones show the
accuracies using only the meta-training set (each row rep-
resents the test accuracy of a single set from the meta train-
ing set). These accuracies are reported here to show the
success of the training phase, while the lower four rows of
the table show the predictive accuracies of the FuAGGE-
classifier for sets that were part neither of the training, nor
of the validation phase.
After the grammar has been created, the data prepared,
and the implementation and testing phases launched, the
system proved its ability to produce rule learners that are
competitive with manually designed learners. We can
clearly see the performance of these formers in Table 1.
We should clarify that these accuracies were calculated by
averaging the accuracies of the fuzzy rule model generated
by the FuAGGE-classifier for each test set over the 10 iter-
ations of the 10-fold-cross-validation method used during
experiments. This also applies to the rest of the benchmark
rule based learners used for purpose of comparison. It is
worth mentioning that in Table 1, the new generated fuzzy
learners has almost the same results as the other methods,
and if we compare only the baseline methods with each
other’s we can clearly notice that the Fuzzy CN2 records
5 wins over 1 for Furia even though Furia is more sophis-
ticated: It uses a growing, pruning and optimization phase
just like the crisp version RIPPER and a fuzzy rule stretch-
ing method. Now if we look at the FuAGGE-classifier
accuracies, we can notice how close these accuracies are
to the baseline algorithms accuracies, which is very inter-
esting due to the fact that the FuAGGE-classifier is auto-
matically generated, and this removes a great deal of hu-
man time coding tasks. Human designers can easily go
wrong when parameterizing an algorithm during the design
process, contrariwise the chance of having wrong parame-
ters when using automatic evolution of algorithms is very
low. The last four rows show that the FuAGGE- classifier
records 1 win against the baseline classifiers (Puba), and an
equality with Fuzzy CN2 (Haberman). For the Ion dataset,
the FuAGGE results are very close to the best accuracy
(90.38% versus 91.17%). These results prove that the pro-
FuAGGE: A Novel System to Automatically. . . Informatica 40 (2016) 237–244 241
Figure 2: The Fuzzy Set Covering Grammar.
Figure 3: Integer Arrays to a Java Code Mapping Process.
posed approach is very promising. However, the FuAGGE
system is time consuming while evolving FuAGGE clas-
sifiers and requires high computational power. Actually, if
run on an ordinary computer, the evolution process can take
up to one week of continuous calculation. We should also
note that this version of the system does not handle miss-
ing values. The system eliminates instances with missing
value before using the datasets. We should also note that
this version uses only numeric attributes. And finally, the
data has been fuzzified manually which is really time con-
suming . This should be tackeled in the next version of
the system by giving it the ability to handle missing values
either by replacing missing values with the mean or me-
dian of the current class, or by the most common attribute
values. We could also give the system the ability to auto-
matically fuzzify data, this can be done simply by coding
the steps required to fuzzify the data, or by following a
method proposed by Swathi et al. [29, 30] which converts
numerical attributes into fuzzy membership functions using
fuzzy clustering. Swathi et al. [30] presented two heuris-
Table 1: Accuracy rates (%) using both meta-sets.
Furia Fuzzy-CN2 FuAGGE Classifier
Iris 92.06 95.20 95.13
Pima 75.65 79.10 60.20
Glass 69.63 65.90 70.43
Wine 65.82 97.90 59.81
Vehicle 70.57 73.30 73.58
Wbc 95.28 98.11 96.26
Ecoli 83.63 83.90 79.82
Ion 91.17 89.50 90.38
Puba 67.83 57.44 70.10
Haberman 72.55 72.92 72.91
tic algorithms for the estimation of parameterized family of
membership functions, namely, triangular and trapezoidal.
Table 2 presents the accuracies of rule-based learners
generated using our proposed system AGGE [31] in the
first column, and those generated using the fuzzy exten-
242 Informatica 40 (2016) 237–244 R. Mazouni et al.
Figure 4: Modules of the proposed system.
AGGE Classifier FuAGGE Classifier
Iris 95.09 95.13
Ion 88.14 90.38
Pima 75.34 60.20
Wine 92.03 59.81
Vehicle 90.03 73.58
Glass 62.69 70.43
WBC 94.93 96.26
Ecoli 73.24 79.82
Haberman 67.45 72.81
Puba 76.44 70.10
sion presented in this paper FuAGGE in the second col-
umn. It is worth noting that the parameters were set as fol-
lows: generations=60, population size=150, crossover=0.8,
mutation=0.1, for both AGGE systems. The upper 6 rows
represent the accuracies using the meta training set, and
the lower rows the accuracies using the meta testing sets.
We notice that even though the grammar used for the
FuAGGE system is very straightforward, the system’s clas-
sifiers recorded 7 wins versus 3 wins for the crisp AGGE
classifiers. This is due to the efficiency of fuzzy systems
versus crisp ones in the classification domain. FuAGGE
proves to be more interesting than AGGE in terms of the ef-
ficiency of its generated classifiers. However, if the number
of generations or the mutation and crossover rates are too
high, we might lose the efficiency of the system because of
the destructive nature of its operators. Accordingly, setting
AGGE and FuAGGE parameters is highly sensitive.
6 Conclusion
In this paper we present a new approach able to automat-
ically produce fuzzy rule-based learners. The system is
mainly based on a BNF context free grammar representing
the overall structure of the baseline fuzzy rule learners. It
also applies the concept of Grammatical Evolution to pro-
duce the best fit rule learner. Experiments on a commonly
used data benchmark show that it is possible to automat-
ically produce rule learners that can compete with manu-
ally designed ones, even with a basic grammar. This is
of great importance, because the proposed method reduces
the burden of writing manually thousands of lines of source
code, and offers a better parameterizing of programs. Our
method can be easily extended to a wide range of appli-
cations, provided that sufficient related data is available.
This may open interesting opportunities and new trends in
data mining and computational intelligence. For instance,
our system could produce rule based learners dedicated to
medical data, biological data, or physics and engineering
data. Algorithms would be parameterized in a way to bet-
ter fit a specific domain and as a result, would achieve more
accurate results in this particular field. Another way of ex-
tending the system is to change the grammar to make the
system capable to generate other data mining algorithms,
such as clustering or fuzzy clustering algorithms.
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