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International Journal of Innovative Technology and Exploring Engineering (IJITEE)
ISSN: 2278-3075, Volume-8 Issue-10, August 2019
4301
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number J10660881019/19©BEIESP
DOI: 10.35940/ijitee.J1066.0881019
Abstract: As the technology improving, the problems of
mankind, regarding health issues also increasing day by day.
Nowadays high dimensionality data are available for various
health problems which is very difficult to handle manually. The
aim of this paper is to construct algorithms for extracting the
relevant information from the large amount of data and
classifying using various hybrid techniques like Fuzzy-Rough set
and Fuzzy Evolutionary Algorithms. The efficiency of Fuzzy
classifiers has been improved by hybridization method. This
paper proposes a comparison of fuzzy hybrid techniques like
Fuzzy Rough set and Fuzzy EA for the diagnosis of Hepatitis
taken from UCI repository. The results of comparison and
classification shows that the proposed technique performs better
than other normal methods.
Keywords: Fuzzy logic, Rough sets, Evolutionary algorithms,
Hybrid techniques
I. INTRODUCTION
In machine learning area, one of the major problems is
classification. It is based on supervised learning process.
From this process, rules can be framed which is used for
prediction. When the number of attributes are raises, the
number of rules also get increased [1].The classification rate
suffers when the number of training data cases is smaller
than the number of attributes [2]. In this paper, we focus on
hybridization of fuzzy with rough set and genetic algorithms
and classification done.
II. MACHINE LEARNING METHODS
Fuzzy Sets and Logic
The idea of Fuzzy set was developed by Mathematician
Lofti Zadeh in 1960’s, is a best tool in mathematics to
manage the uncertainty that arises due to impreciseness for
solving the problem. Mathematically, a fuzzy set A is
defined to be a set of ordered pairs and is written as
A = {(x, μA(x)) | x € X},
Where X is the universe of discourse and μA(x) is called
the membership function of x in A. In order to deal with
reasoning problem, multi valued logic that is derived from
Fuzzy set theory known as Fuzzy logic has been applied [3].
Revised Manuscript Received on August 05, 2019
S. Poongothai, Asst. Professor, Department of Mathematics, SRM
University, Ramapuram Campus, Chennai, India
C. Dharuman, Professor, Department of Mathematics, SRM University,
Ramapuram Campus, Chennai, India
P. Venkatesan, Faculty of Research, Sri Ramachandra University,
Chennai, India
The main reasons for the development of fuzzy systems
are [4]: (i) Human reasoning is very simple to adapt using
fuzzy system; (ii) Mathematically, models of societal
problems can easily be constructed; (iii) creates transition
between members and non-members easily; (iv) system
fluctuations are less sensitivity; and (v) Description or
linguistic rules can be easily framed by fuzzy system. In this
paper, FURIA (Fuzzy Unordered Rule Induction Algorithm)
is considered for classification. Based on RIPPER
algorithm, FURIA is developed. This method is well versed
in differentiating and separating the classes and so there is
no use of default rule and the classes order are irrelevant [5].
Rough Sets
In 1980’s Zdzislaw Pawlak [6] proposed a new method
called Rough set which is another mathematical tool used to
handle vagueness and imprecise. In this approach,
uncertainty and impreciseness are not expressed by the
membership functions as in fuzzy sets but defined by the
boundary region of a set. The major difference of these two
approaches are fuzzy sets are employed with membership
function, where Rough sets are defined by topological
operations called upper approximations and lower
approximations, that requires advanced mathematical
concepts. It is used to find the reduct set of attributes from
large set of data present in the decision system. This reduct
set then used to frame rules for classification through data
mining techniques. Let U be the universe, a nonempty finite
set of M objects, {y1, y2,y3,… ym}, Q be the finite set of
attributes, then the information system is defined as
where
i.e.,
is the domain for attribute q
and is the information function such that
for every
Indiscernibility Relation (IR) on U is defined as
Where is the set of attributes. The decision table
is defined as , where C and D are the
condition attribute and the decision attribute respectively,
and is the decision
function such that
for every For a
given space S, a subset determines the
approximation space as in S. For a given
and , the upper and lower approximations of
are defined respectively as
Performance of Fuzzy Rough Sets and Fuzzy
Evolutionary Classifiers using Medical Databases
S. Poongothai, C. Dharuman, P. Venkatesan
Performance of Fuzzy Rough sets and Fuzzy Evolutionary Classifiers using Medical Databases
4302
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number J10660881019/19©BEIESP
DOI: 10.35940/ijitee.J1066.0881019
The two major concepts of Rough set theory are core and
reduct which is used for selecting feature attributes as well
as reducing the attributes. In the information system, some
attributes are redundant with respect to that is generated
by attributes . Based on attributes qualities, it is
possible to find irrelevant attributes and also we can remove
those attributes, without affecting the classification
accuracy. If then the attribute
is considered as dispensable in the set A i.e.,
indiscernibility relation of and are same. If it is
not identical, then is indispensable in These dispensable
attributes are not used to improve the accuracy of
classification of IS. All indispensable attributes together
forms the set called Core of and it is denoted by
If all the attributes in the set are indispensable,
then the set A is called orthogonal. Also if there exists a
proper subset that is orthogonal and also preserves
the classification, then it forms the reduct set generated by
. Hence a reduct set of , is denoted by , is defined
as ,
where E is a reduct of A [6]. Also the reduct set cannot be
further reduced.
Evolutionary Algorithms
In 1960 I. Rechenberg introduced the idea of Evolutionary
Algorithms in his work “Evolutionary strategies”. EAs are
algorithms of general class stochastic optimization based on
neo-Darwinian theory. The main idea behind EAs are
Survival of the Fittest [7]. Most common Evolutionary
Operators are Selection, Crossover and Mutation. The main
four streams of EAs are (i) Evolutionary Programming by
Fogel et al., in 1966 (ii) Evolutionary Strategies by
Rechenberg in 1973 (iii) Genetic Programming by Holland
in 1975 (iv) Genetic Algorithms by Holland in 1975. In the
proposed method genetic algorithms is used for feature
selection. It is a global search technique applied widely to
optimize the problems (Holland, 1975) [8]. It can also be
used for solving the problems having objective function as
discontinuous, stochastic, non linear or non-differentiable
[9].
III. ALGORITHMS FOR HYBRIDIZATION
Fuzzy Rough Sets
Fuzzy Rough sets is the generalization of rough set s
having fuzzy background i.e., to obtain results of fuzzy in a
crisp space [10-12]. This model is mostly utilized in
knowledge acquisition with decision tables of real valued
conditional attributes and reasoning [13–20]. In this case the
decision attribute values are termed as fuzzy and the
conditional attribute values are termed as crisp value. The
major role of this model is to define the lower and upper
approximation of the set. Let U and V be two nonempty
universe discourse set and R be a fuzzy relation from U to
V, then the generalized fuzzy approximation space is
denoted by the triple (U, V, R). When U equals V and R
defined a fuzzy relation on U, then (U, R) is termed as a
fuzzy approximation space. The membership value of 1, 0.5
and 0 are for elements having lower approximation (positive
region), boundary region and upper approximation (negative
region) respectively [21]. Using Fuzzy partition, the input
set X is partitioned into N clusters named C1, C2,…,CN be
generated [22]. Each equivalence class having output classes
in various forms is denoted by each cluster. These output
classes are identified by fuzzy upper and lower
approximations equivalence classes. Let (U, R) be a
approximation space and μ F(U). The lower is expressed
as
R
(μ) and upper rough approximations of μ in (U, R) are
expressed as
R
(μ), which are fuzzy subsets in U defined by
for all x U. μ is called definable in (U, R) if
R
(μ) =
R
(μ), otherwise it is a rough fuzzy set [23]. Fuzzy-Rough
Feature Selection (FRFS) used effectively for real valued or
discrete noisy data to reduce the attributes without the need
for user-supplied details. Each feature required to be in the
form of fuzzy partition that can be derived from the data
itself.
Fuzzy Genetic Algorithm
The power of Fuzzy Rule Based Systems (FRBS) which
is an extension of classical rule based systems that are
dealing with “IF-THEN” rules, its antecedents and
consequents are represented by fuzzy logic statements are
described for solving modelling problems, control problems,
data mining problems [24-26], in numerous application
areas. Fuzzy genetic algorithm is a fuzzy system augmented
by the process of learning based on evolutionary
computation. A fuzzy representation is proposed for
handling the optimization problems of parameters whose
variables are continuous domains. Each parameter in the
problem is associated with a number (m) fuzzy decision
variables which belongs to the interval [0,1] [27]. Each
parameter is linked with the values of the decision variables
to get the solutions. The workflow of this process is shown
in figure 1.
Fig. 1 Fuzzy Genetic method
International Journal of Innovative Technology and Exploring Engineering (IJITEE)
ISSN: 2278-3075, Volume-8 Issue-10, August 2019
4303
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number J10660881019/19©BEIESP
DOI: 10.35940/ijitee.J1066.0881019
Description of datasets
The proposed method is used to classify the dataset of
Hepatitis disease taken from UCI machine learning
repository. The number of instances and attributes are 155
and 20 respectively. The aim is to classify the death and live
due to presence of hepatitis [28].
IV. RESULTS
In the proposed method, each attribute Ai in a rule can be
expressed in the form ( ), if the selector is Ai ≤ v, then
I is an interval (-∞, v], if the rule selector is Ai ≥ u then I is
an interval [u,∞), and I = [u, v] if it contains both Ai ≤ v and
Ai ≥ u, the fuzzy intervals obtained by trapezoidal
membership function replaces the intervals [5]. For rough
set, the data which has taken is stored in a table, called
decision table. Rows represents objects and columns
represents attributes. Rough set theory defines three regions
namely lower, upper and boundary approximations. All the
objects that are positively classified contained in Lower
approximation, the probably classified objects contained in
upper approximation, while the boundary is the difference
between these two approximations. But in the method of
GA, by selecting individuals (attributes) from the current
population (Dataset) randomly and uses them to produce
new offsprings for the next generation. After applying
crossover and mutation, several generations obtained by
GA, it tries to give the optimal solution. At last the lowest fit
individuals in the original population are replaced by the
newly created offsprings. This replacement always gives the
best set of individuals deleting the worst ones. The solution
obtained by each generation is better than its previous one.
The iterations can be continued till the stopping criteria or
the desired result obtained [5].In this paper, Fuzzy, Fuzzy
rough set (FRS) and Fuzzy Genetic Algorithms (FGA) are
used to classify the database. Using the FRS the attributes
are reduced to 13 and it is shown in figure 2. The
classification rate for this system is 81%.
Fig. 2 Fuzzy rough feature selection
Fig. 3 Feature selection by GA
Fig. 4 Confusion matrix of fuzzy classification
By the second method the attributes are reduced to 5 and
87% correctly classified. Reduced attributes by GA is shown
in figure 3. The confusion matrix of this model is given in
figure 4. Also the classification of Fuzzy alone has been
discussed and given in figure 5 which gives only 79.35%
classification.
Fig. 5 Classification of Fuzzy
V. DISCUSSIONS AND CONCLUSIONS
In this paper, fuzzy rough and fuzzy genetic methods are
compared for classification for Hepatitis. Also along with
these hybrid methods, Fuzzy is compared and this paper has
shown that the idea of hybridization of genetic algorithm
Performance of Fuzzy Rough sets and Fuzzy Evolutionary Classifiers using Medical Databases
4304
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number J10660881019/19©BEIESP
DOI: 10.35940/ijitee.J1066.0881019
with fuzzy sets in a fruitful way. The following table 1
shows the comparison of the proposed model of the paper.
Table. 1 Comparison of Classification
Method of
Classification
No. of
Attributes
Classification
rate (%)
Fuzzy
20
79.35
FRS
13
81
FGA
5
87
This shows hybridization role plays in a better way
compared to concept of fuzzy alone. Out of these two hybrid
methods, FGA is good in classification. The idea of
differential evolutionary algorithm shall be combined with
fuzzy sets for future works.
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