Effective Method for Extracting Rules from Fuzzy Decision Trees based on Ambiguity and Classifiability by UniCSE

VIEWS: 424 PAGES: 9

More Info
									  Universal Journal of Computer Science and Engineering Technology
  1 (1), 55-63, Oct. 2010.
  © 2010 UniCSE, ISSN: 2219-2158

    Effective Method for Extracting Rules from Fuzzy
         Decision Trees based on Ambiguity and
                     Classifiability
          Hesham A. Hefny                                Ahmed S. Ghiduk                                  Ashraf Abdel Wahab
  Dept. of Computer and Information               Dept. of Mathematics, Faculty of                   Dept. of Computer and Systems,
   Sciences, Institute of Statistics,              Science, Beni-Suef University,                     Electronics Research Institute,
       Cairo University, Egypt.                          Beni-Suef, Egypt.                                    Cairo, Egypt.
        hehefny@hotmail.com                           asaghiduk@yahoo.com                                 awahab@mcit.gov.eg



                                                        Mohammed Elashiry
                                                       Dept. of Management,
                                                   Academy of Specialized Studies,
                                                         Beni-Suef, Egypt.
                                                        ashiry@aun.edu.eg

Abstract—Crisp Decision trees (CDT) algorithms have been the              Fuzzy Gain Ratio and Fuzzy Ambiguity to split the instances at
most widely employed methodologies for symbolic knowledge                 each node [4,17,18] while the other algorithms such as
acquisition. There are many methodologies have been presented             classifiability of instances are based on pruning the decision
to address the problems of the continuous data, multi-valued              tree [1,17].
data, missing data, uncertainty data and noisy features. Recently,            Both of Fuzzy Information Gain (FIG) and Fuzzy Gain
due to the widespread use of the fuzzy representation, a lot of           Ratio (FGR) algorithms use the concept of entropy to reduce
researchers have utilized the fuzzy representation in decision            the depth of the fuzzy decision tree by determining the
trees to overcome the preceding problems. Fuzzy decision trees            quantitative value of the uncertainty in each attribute of a data
(FDT) are generalization for the CDT. FDTs are built by using
                                                                          set. FIG and FGR are suitable for originally categorical data.
fuzzy or crisp attributes and classes which often need pruning to
reduce their size. FDTs have been successfully used to extract
                                                                          The drawbacks nodes within the hidden level are generated
knowledge in uncertain classification problems. In this paper, we         until the fuzzy entropy is reduced to zero [3,4,5,6,
present a technique to build FDT by employing the ambiguity of            7,9,10,11,12,13,16,17].
attributes and classifiability of instance. Our technique builds a            Fuzzy ambiguity algorithm is based on the possibility to
reduced FDT which does not need for applying the pruning                  find the ambiguity in each attribute. Fuzzy ambiguity algorithm
algorithms to reduce the size. The paper also presents the results        is suitable for numerical and categorical data. Fuzzy ambiguity
of a set of empirical studies conducted on a dataset of UCI               algorithm is more accurate than fuzzy entropy algorithm in
Repository of Machine Learning Database that evaluate the                 finding the uncertainty attribute, directly measure the quality of
effectiveness of our technique compared to Fussy Iterative                classification rule in decision node, significant level which will
Dichotomiser 3 (FID3), ambiguity, and FID3 with classifiability           affect the generation of FDT [4, 11, 12, 16, 17, 18].
techniques. The studies show the effective of our technique in                Fuzzy Information Gain, Fuzzy Gain Ratio, and Fuzzy
reducing the number of the extracted rules without loosing of the         ambiguity select and isolate a single attribute for building the
rules accuracy.                                                           decision tree without considering the other related attributes.
                                                                          Thus, the decision tree needs to burn for reducing the number
  Keywords-Fuzzy decision tree; Fuzzy entropy;              Fuzzy         of the extracting rules[3,4,5,7,9,10,11,12,13,14,16,18, 22].
Ambiguity; Fuzzy rules; Classifiability of Instances.                         Classifiability algorithm selects an attribute with
                                                                          considering the instances in the other attributes. Classifiability
                       I.    INTRODUCTION                                 algorithm is considered a decision tree pruning technique.
    FDT is an extension to the crisp decision tree which is               Therefore, it improves the performance of decision making,
based on fuzzy valued attributes and classes. FDT has the                 accurate prediction, efficiency and comprehensibility of the
ability for dealing with ambiguity and vagueness attributes               generated useful rules to electric power companies [1, 6].
associated with human thinking as well as crisp attributes.                   Finally there are two stages to extracting rules from dataset,
    A lot of algorithms have been proposed for producing small            firstly create Fuzzy Decision Tree, secondly pruning a tree, our
size decision trees [1,4,17,18]. Some of these algorithms use             proposed will be reduced the steps also, reduce tree size and
different criteria such as: Fuzzy Entropy (Information Gain),             enhanced accuracy with using an algorithm.


                                                                     55
  Corresponding Author: Hesham A. Hefny, Dept. of Computer and Information Sciences, Cairo University, Egypt.
                                                       UniCSE 1 (1), 55 -63, 2010

    All the previous techniques contain two stages for                          G(Am(k)) = g ( Π (C | Am(k))), which is measured based on
extracting rules from a dataset. The first stage creates fuzzy              the Possibility Π (C|Am(k) ) .
decision tree. The second stage prunes the fuzzy decision tree
to reduce the size of the tree.                                             C. Compare between Fuzzy -ID3 and Fuzzy Ambiguity
    In this paper, we present a technique to build FDT by                     1) Properties Fuzzy ID3
employing the ambiguity of attributes and classifiability of                    Entropy determines the quantitative value of the
instance. Our technique builds a reduced FDT which does not                      uncertainty carried by each attribute in a data set but not
need for applying pruning algorithms to reduce the size. The                     the whole data set [6, 19].
paper also presents the results of a set of empirical studies                   The nodes within the hidden level are generated until the
conducted on a dataset of UCI Repository of Machine Learning                     fuzzy entropy is reduced to zero [18].
Database that evaluate the effectiveness of our technique                       That heuristic attempts to reduce the average depth of
compared to Fussy Iterative Dichotomiser 3 (FID3), ambiguity,                    tree [5,3].
and FID3 with classifiability techniques. The studies show the                  E(Aki)= -Σ j = 1,mcPkijlog2Pkij and minimum fuzzy entropy
effective of our technique in reducing the number of the                         is selected [3].
extracted rules without loosing of the rules accuracy.                          If Pkij = 0 or 1 then Entropy(u) = 0 [18].
    The rest of the paper is organized as follow. Section II gives              Method is more suitable for originally categorical data.
some basic concepts and definitions. Section III introduces a                 2) Properties Fuzzy Ambiguity
number of the problems of the control dependencies based
                                                                                Directly measure the quality of classification rule in
fitness function and presents two schemes and the key
                                                                                 decision node [18].
ingredients to overcome these problems. Section IV provides
the related work. Section V gives conclusions and future work.                  An option of significant level which will effect the
                                                                                 generation of FDT [3].
                      II.       BASIC CONCEPTS                                  That heuristic attempts to reduce the average depth of
                                                                                 tree [3].
   This section gives some basic concepts. There are some of                                                   nc *
                                                                                                                      *
                                                                                                                                           
heuristic proposed to generate roles next subsection displays                                     G ( Aik )      
                                                                                                                    s
                                                                                                                                            ln s
                                                                                                                                           
                                                                                                                       s 1
some of them as the following:                                                                                s 1                        
A. Information Gain                                                             Minimum Fuzzy ambiguity implies to minimum fuzzy
                                                                                 entropy [3, 4, 12].
     The earlier version of ID3 which is based on minimum                       Π(x) = 1 mean x is fully possible and Π (x) = 0 mean x
information entropy to select expand attributes. This heuristic                  is impossible
is an improved heuristic of famous ID3, information gain used                                        Π*2 =0 Ambig=0
the machine learning using decision tree in calculating                                            Π*n =1Ambig=Ln(n)
significance of attributes [11, 8, 7, 9, 15].                                    Minimum Fuzzy ambiguity Implies to Minimum Fuzzy
     Consider a non-leaf node S consisting of n attributes A(0)                  Entropy
,...,A(n) to be selected. For each k (1 ≤ K ≤ n), the attribute A(K)
                                                                                Method is more suitable for originally numerical data.
takes mk values of fuzzy subsets, A1(K),...... Am(k) and the fuzzy
classification is A(C) .                                                    D. Classifiability of attribute by instances
     The averaged fuzzy classification entropy of the k-th                      Decision tree pruning is useful in improving the
attribute is defined as:
                                                                          generalization performance of decision trees. The criteria is
                                                                          based on Classifiability measure , that considers the number of
                       m  M ( Ai      ) 
                                  (K )
              Ek  i 1  m
                      k

                                          Entri
                                                 k
                                                      (1)                   pattern instances of different classes at node and spatial
                            M ( Aj ) 
                            k
                                      k                                     distribution or these instances to estimate the effect of further
                                        
                           j 1                                           splitting the node [6] .
where, Entri(k)= -Σj=1,mcPij(k)log2Pij(k); 1≤k≤n; 1≤i≤mk; 1≤j ≤mC.              L(k) is measure of Classifiability of attribute K within
     Fuzzy ID3 heuristic aims to search for an attribute such that          instances given by:
                                                                                                   C                  C       C
its averaged fuzzy classification entropy attains minimum, i.e.
selecting such an integer k0 (the k0-th attribute) that Eko =
                                                                                       L( k )    w
                                                                                                   i 1
                                                                                                           (k )
                                                                                                           ii     -    w
                                                                                                                      i 1   i 1
                                                                                                                                    (k )
                                                                                                                                    ii              (3)
Mini<k<n(Ek).                                                                                                                ji
                                                                                Since W is Local co-occurrence matrix after attribute k is
B. Minimum Classification ambiguity                                         selected calculated as:
                                                                                                    mk
                                                                                       W (K )            
    Instead of using minimum fuzzy entropy [18, 11, 4, 12, 2]
this heuristic uses the minimum classification ambiguity to                                                           P( x)                         (4)
select expanded attributes. The classification ambiguity with                                       i 1     x
                                                                            where x is any instance in the i-th child node of current node.
fuzzy attribute A(k) is               
                                                                              P(X) is Local co-occurrence matrix for instance x. It
                                           
                      mk          (A k ) 
                                                                            capture the distribution of instances around a specific instance,
                                      i    
           G ( Ak   )                         k
                                            G(A i )       (2)              the size of Local co-occurrence matrix is C x C since C is
                               mk        k)
                      i 1         (A                                   number of classes, as in eq.(5)
                                                                                                                  ( x )T  ( y ) .
                                         j 
                          
                               j 1        
                                                                                    P (x)                                                          (5)
                                                                                                   y ,D x y  r




                                                                       56
                                                         UniCSE 1 (1), 55 -63, 2010

    pij = Σ y, Dxy≤ r μi(x) μj(y) of matrix P show the number of                 Level (2) : Repeat steps of level (1) to create level (2) of
class j instance that are within the neighborhood r of instance                    tree and so .
x when instance x belongs to class I within membership μi(x)
    Distance between instances defined by                                     B. Flow Chart of Proposed Fuzzy Decision Trees
                  n   mk                                                          The algorithm aims to generate fuzzy decision trees based
       Dxy     i( k ) ( x)   i( k ) ( y )       (6)                     on minimum objective function, see equation (7), of each
                 k 1 i 1                                                    attribute in dataset. The objective function J measures pure
    For any instance in the data set, we can find those instances             ambiguity of attributes by eliminating classifiability of
that are within a circular neighborhood r, Membership values                  attributes from ambiguity of attributes. Figure 3.1 shows the
of instance x for classes µ(x) = [µ1(x), , µ(x)].                             flow chart of the AMCL proposed algorithm.
    For example P(X=1) for A12 (sub attribute 2 of attribute 1),
mean Local co-occurrence matrix for instance X=1, remove all                                                           Start
instances have zero value in A12, find all distance between
instance X=1 and X={1,…, N}, choose instances with                                                         Read attributes, classes
neighborhood less than or equal r of instance X=1 and sum
results of multiply vectors which represent membership of
classes of instance X=1 and neighborhood instance. Repeat that                                         No              An             Yes
                                                                                                                                               End
                                                                                                                    attribute
for all instances and attributes.
    J (k) = any measure of classification – L (k)       (7)
                                                                                                   One
          III. THE PROPOSED FUZZY DECISION TREES                                                   Class
                                                                                                                  Yes
                                                                                                                          End
      CLASSIFIABILITY OF INSTANCES AND AMBIGUITY OF
                             ATTRIBUTES                                                       No

     Aim to build tree with both of the ambiguity of attributes                              For k=1, n
                                                                                                                  End
                                                                                                                                For k=1, n
                                                                                                                                                    End For
                                                                                                                 For
and Classifiability of instances.                                                            attributes                         attributes

A. Proposed of heuristic fuzzy ambiguity with classifibility                            Compute G (Ak)                     Aroot =min (J(Ak))
    "AMCL"
         Through following levels fuzzy decision tree was                              Compute L (Ak)
                                                                                                                        Delete all empty branches of
                                                                                                                                    Aroot
creating as:
    Level (-1):                                                                          k         k        k
                                                                                      J(A ) = G (A ) - L (A )
                                                                                                                                                    End
                                                                                                                                                              For each branch of
                                                                                                                                                                                    End
                                                                                                                           For I =1, m Branch of
      1- Consider a non-leaf node S consisting of n attributes                                                                      Aroot
                                                                                                                                                    For       Aroot which has not   For End
          A(0) ,...,A(n) to be selected. For each k (1 ≤ K ≤ n), the                                                                                                  leaf

          attribute A(K) takes mk values of fuzzy subsets,                                                       End
                                                                                                                 For           For J=1, C                      Compute G (Ak| Arooti) for
          A1(K),...... Am(k)                                                                                                    classes                       each k attribute where order
    Level (0):                                                                                                                                                           k ≠ root
      1-For all Attribute A(K) calculate G(A(K)) and L(A(K)) ,1                                                        Compute X=S (branch of Arooti              Compute L(Ak| Arooti )
          ≤ K ≤ n them compute objective function J(A(K)) =                                                                     ,Classj )                       for each k ≠ root attribute
                                                                                                             Z is
          G(A(K)) - L(A(K))                                                                     Yes
                                                                                                            empty
                                                                                                                                   If
      2- The root of decision is min{J(A(K))} root is Aroot =                                                                    (X>=β)
                                                                                                                                               No
                                                                                                                                                                  Compute J(Ak| Arooti )
          MIN{ J(A(K)}                                                                                      No
                                                                                                                                                                for each k ≠ root attribute
    Level (1): Delete all empty branches of the decision node.                                     Branch Arooti has a
                                                                                                                                       Yes

      For each nonempty branch of the decision node calculate                                            leaf,                    Array Z =X                                        Branch Arooti has
                                                                                                                                                                                 No class which max
      the truth level of classifying all objects within the branch                                  which have max                                                   IF J(Ak|
                                                                                                                                                                                    S(Arooti,Classes)
                                                                                                       value of Z                                                     Arooti)
      into each class as a leaf, according to the following:                                                                                                           <=
      1- Attribute Aroot =(Aroot1 , ...... , Aroot m ) and classes C=                                                                                                     Ye
                                                                                                                                                                     J(Arooti)
          (C1,C2,...,Cw)                                                                                                                                                  s
                                                                                                                                                      Attributes=Attributes - Root Attribute
                                                                                                                                                         #attributes = #attributes – 1
      2-     Calculate        the    classification      truth   level                                                                                     k
                                                                                                                                                         A is Root of Arooti branch
          S(Aroot1,Cj)classes Cj , 1 ≤ j ≤ w
                                                                               Figure 3.1: Flow chart of the algorithm of the proposed fuzzy decision tree
      3- IF S(Aroot i , Cj ) ,1≤i≤m,1≤j≤ w, greater than truth level
          β THEN Aroot i become a leaf with label Cj                                                              IV.           EXPERIMENTS
          Else Partitioning the branch Aroot i with different
          attributes according to the following:                                   The datasets which have been used for the experiments are
          I-Compute J(Aroot i), J(AK | Aroot i), where 1≤ k ≤ n and           obtained from [8] their features are briefly described in table
             K ≠ root for each K                                              4.1. The next subsections present data sets.
       II-IF J (AK|Aroot i) ≤ J(Aroot i)
           THEN AK is branch from Aroot i
            Else Aroot i leaf with label that have greater value of S
           (Aroot i , Cj )



                                                                         57
                                                                                              UniCSE 1 (1), 55 -63, 2010


                                     TABLE 4.1: THE FEATURES OF DATA SETS                                                            16

                                                                                                                                     14
                                      Datasets        Samples       Attributes       Classes




                                                                                                                Numbers of rules
                                                                                                                                     12

                                     Weather            16                     4          3                                          10

                                 Wisconsin Cancer       699                    9          2                                                8

                                      Monk              432                    7          2                                                6
                                                                                                                                           4
                                       Iris             150                    4          3
                                                                                                                                           2
                                  Pima diabetes         768                    8          2
                                                                                                                                           0
    Tree Quality Measures; in all the following data sets,                                                                                     0.5         0.6         0.7               0.8                  0.9            1
                                                                                                                                                                            Thre shol d (β)
calculate tree quality using two measures:                                                                                                                        AM         AMCL             IG             IGCL

     Size of tree is number of leaf nodes (number of rules).                                                 Figure 4.1.e: Number of rules for AM, AMCL, IG and IGCL with α = 0.3
     Classification accuracy of rules.                                                                            In addition, comparison between IG, IGCL, AM and
A. Weather Dataset of Quinlan’s                                                                               AMCL from figure 4.2, which summarized in table 4.2, the
                                                                                                              size of tree AMCL is smaller size than IG, IGCL and AM.
   The following sections compare between algorithms fuzzy                                                                                     88
ID3 "IG", fuzzy ID3 with classifiability "IGCL", fuzzy                                                                                         86
                                                                                                                                               84
ambiguity denote as "AM" and a new heuristic fuzzy ambiguity                                                                                   82
                                                                                                                                               80
with classifibility "AMCL". Set of rules and the accuracy are




                                                                                                                         Accuracy
                                                                                                                                               78
                                                                                                                                               76
summarizes in figure 4.1 with different value of fuzzy filter α.                                                                               74
                                                                                                                                               72
                          18                                                                                                                   70
                          16                                                                                                                   68
                                                                                                                                               66
                          14
                                                                                                                                               64
       Numbers of rules




                          12
                                                                                                                                                0.5         0.6         0.7               0.8                 0.9                1
                          10                                                                                                                                                 Th re sh ol d (β)
                                                                                                                                                                  AM          AMCL               IG           IGCL
                           8
                           6
                                                                                                              Figure 4.1.f: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.3
                           4
                                                                                                                                                18
                           2                                                                                                                    16

                                                                                                                            Numbers of rules
                           0                                                                                                                    14
                                                                                                                                                12
                               0.5         0.6        0.7            0.8           0.9             1                                            10
                                                        Thre shol d (β)
                                                 AM         AMCL            IG     IGCL                                                          8
                                                                                                                                                 6
  Figure 4.1.a: number of rules for AM, AMCL, IG and IGCL with α = 0.1                                                                           4
                          84
                                                                                                                                                 2
                                                                                                                                                 0
                          80
                                                                                                                                                    0.5     0.6         0.7              0.8                 0.9             1
                                                                                                                                                                            Thre shol d (β)
      Accuracy




                          76
                                                                                                                                                            AM               AM CL                    IG              IGCL

                          72
                                                                                                              Figure 4.1.g: Number of rules for AM, AMCL, IG and IGCL with α = 0.4
                          68
                                                                                                                                                96
                                                                                                                                                92
                          64                                                                                                                    88
                                                                                                                            Accuracy




                               0.5         0.6        0.7            0.8           0.9             1                                            84
                                                        Th re sh ol d (β)                                                                       80
                                                 AM         AMCL            IG     IGCL                                                         76
                                                                                                                                                72
Figure 4.1.b: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.1                                                                           68
                                                                                                                                                64
                                                                                                                                                60
                          16

                          14                                                                                                                         0.5    0.6         0.7              0.8                 0.9             1
                                                                                                                                                                            Thre shold (β)
     Numbers of rules




                          12
                          10                                                                                                                                 AM              AM CL                    IG              IGCL
                           8
                           6                                                                                  Figure 4.1.h: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.4
                           4
                                                                                                                 90
                           2                                                                                     80
                           0                                                                                     70
                                                                                                                 60
                               0.5         0.6        0.7            0.8
                                                        Thre shol d (β)
                                                                                   0.9            1              50
                                                                                                                 40
                                                 AM         AMCL          IG       IGCL                          30                                                                                        N. Rules
                                                                                                                 20
  Figure 4.1.c:Number of rules for AM , AMCL, IG and IGCL with α = 0.2                                           10
                          80                                                                                      0                                                                                        Traning Accuracy
                          79
                          78
                          77
                          76
                                                                                                                                                     AM    AMCL        IG        IGCL
                          75
                          74
    Accuracy




                          73
                          72
                          71                                                                                   Figure 4.2: Size of tree AMCL is smaller size than IG, IGCL and AM.
                          70
                          69
                          68
                          67
                                                                                                                                                TABLE 4.2: NUMBERS OF RULES AND TRAINING ACCURACY
                          66
                          65
                          64                                                                                                                                                AM                 AMCL                   IG             IGCL
                          63

                           0.5            0.6         0.7           0.8            0.9            1                                             N. Rules                    13                        5               16             13
                                                        Thre shol d (β)
                                                 AM     AMCL              IG       IGCL                          Training Accuracy                                      69.2                       86.1               69             80.4
 Figure 4.1.d: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.2




                                                                                                         58
                                                                                                    UniCSE 1 (1), 55 -63, 2010

B. Wisconsin Breast Cancer (Real World Datasets)
    Mangasarian and Bennett (1996) have compiled data on the
                                                                                                                                                       96
problem of diagnosing breast cancer to test several new                                                                                              95.5
                                                                                                                                                       95
                                                                                                                                                     94.5
classification methods [Merz (1996)].                                                                                                                  94
                                                                                                                                                     93.5
                                                                                                                                                       93
    Each pattern in the data set has nine inputs and an                                                                                              92.5
                                                                                                                                                                                                                                              AM
                                                                                                                                                                                                                                              AMCL




                                                                                                                              Accuracy
                                                                                                                                                       92
associated with class label malignant and benign. Total                                                                                              91.5
                                                                                                                                                       91
                                                                                                                                                                                                                                              IG
                                                                                                                                                                                                                                              IGCL
                                                                                                                                                     90.5
numbers of instances are 699 patients with breast cancer, 458                                                                                          90
                                                                                                                                                     89.5
                                                                                                                                                       89
benign patients and 241 malignant patients, 60% of data for                                                                                          88.5
                                                                                                                                                       88
training and 40% for testing and average of the results obtained                                                                                     87.5
                                                                                                                                                       87
                                                                                                                                                     86.5
are shown in figure 4.3.                                                                                                                               86

                                                                                                                                                        0.5            0.6    0.7          0.8            0.9            1
    Moreover, comparison between IG, IGCL, AM and AMCL                                                                                                                        Th re sh ol d (β)

is shown in figure 4.4 which summarized in table 4.3, illustrate                                                            Figure 4.3.f:Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.3
that size of tree by AMCL is smaller szie than tree from IG,
                                                                                                                                                     120
IGCL and AM algorithms
                                                                                                                                                     100
                                    140




                                                                                                                                  Numbers of Rules
                                    120                                                                                                                80                                                                                AM
                                                                                                                                                                                                                                         AMCL
           Numbers of Rules




                                    100
                                                                                                         AM                                            60                                                                                IG
                                          80                                                             AMCL                                                                                                                            IGCL
                                                                                                         IG                                            40
                                          60                                                             IGCL

                                          40                                                                                                           20

                                          20
                                                                                                                                                        0
                                           0
                                                                                                                                                        0.5            0.6    0.7         0.8            0.9             1
                                              0.5        0.6    0.7         0.8      0.9    1
                                                                                                                                                                              Th re sh ol d (β)
                                                                Th re sh ol d (β)

                                                                                                                            Figure4.3.g:The number of rules for AM ,AMCL,IG and IGCL with α=0.4
 Figure4.3.a: The number of rules for AM,AMCL, IG and IGCL with α=0.1                                                                                   96
                                            96                                                                                                        95.5
                                          95.5                                                                                                          95
                                            95                                                                                                        94.5
                                          94.5                                                                                                          94
                                            94
                                          93.5                                                                                                        93.5
                                            93                                                           AM                                             93                                                                                     AM
                                          92.5                                                                                                        92.5
                                                                                                         AMCL                                                                                                                                  AMCL
                                                                                                                                    Accuracy
                 Accuracy




                                            92                                                                                                          92
                                          91.5                                                           IG                                           91.5                                                                                     IG
                                            91                                                                                                          91
                                                                                                         IGCL                                                                                                                                  IGCL
                                          90.5                                                                                                        90.5
                                            90
                                          89.5                                                                                                          90
                                            89                                                                                                        89.5
                                          88.5                                                                                                          89
                                            88                                                                                                        88.5
                                          87.5                                                                                                          88
                                            87                                                                                                        87.5
                                          86.5
                                            86                                                                                                          87
                                                                                                                                                      86.5
                                                                                                                                                        86
                                                0.5       0.6    0.7         0.8     0.9    1
                                                                 Th re sh ol d (β)
                                                                                                                                                            0.5         0.6     0.7          0.8           0.9               1
 Figure 4.3.b: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.1                                                                                                          Th re sh ol d (β)
                                          140                                                                               Figure 4.3.h: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.4.
                                          120
                                                                                                                               110
                       Numbers of Rules




                                          100                                                                                  100
                                                                                                         AM
                                              80                                                         AMCL                   90
                                                                                                         IG                     80
                                              60                                                         IGCL                   70
                                              40                                                                                60
                                              20
                                                                                                                                50
                                                                                                                                                                  AM            AMCL                      IG                     IGCL
                                               0

                                                0.5       0.6    0.7         0.8     0.9    1                                                                     N. Rules    Traning Accuracy                   Test Accuracy
                                                                 Thre shol d (β)
                                                                                                                                Figure 4.4: the accuracy and size of tree of IG, IGCL, AM and AMCL
 Figure 4.3.c: The number of rules for AM,AMCL,IG and IGCL with α=0.2                                                        Table 4.3: Numbers of rules, training and testing accuracy
                                                96
                                              95.5
                                                95
                                              94.5
                                                                                                                                                                              AM             AMCL                 IG              IGCL
                                                94
                                              93.5
                                                93                                                      AM                                              N. Rules              100                 91              102              95
                                              92.5                                                      AMCL
                              Accuracy




                                                92
                                              91.5
                                                91
                                                                                                        IG                          Training Accuracy                         95.2                95.7            95.1            95.3
                                                                                                        IGCL
                                              90.5
                                                90
                                              89.5                                                                                                   Test Accuracy            95.6                96.1            95.6             96
                                                89
                                              88.5
                                                88
                                              87.5
                                                87
                                              86.5
                                                                                                                           C. Dataset of Monk_1 Problem
                                                86

                                                   0.5    0.6    0.7         0.8     0.9    1
                                                                                                                               Number of instances is 432, number of attributes is 8
                                                                 Th re sh ol d (β)
                                                                                                                           including class attribute. Information of attributes is [8]:
 Figure 4.3.d: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.2
                              120
                                                                                                                              1. Id                           unique symbol for each instance 2. A1                  1, 2, 3
                              100                                                                                             3. A2                           1, 2, 3                                     4. A3        1, 2
   Numbers of Rules




                                     80                                                                        AM
                                                                                                               AMCL
                                                                                                                              5. A4                          1, 2, 3                                     6. A5 1, 2, 3, 4
                                     60                                                                        IG
                                                                                                               IGCL           7.A6                           1, 2                                        8.Class 0, 1
                                     40

                                     20                                                                                       Missing Attribute Values: None
                                          0                                                                                   Target Concepts associated to the MONK-1 problem (a1 =
                                           0.5           0.6    0.7          0.8      0.9       1                          a2) or (a5 = 1). 60% of data for training and 40% for testing
                                                                Th re sh ol d (β)


  Figure 4.3.e: The number of rules for AM,AMCL,IG and IGCL with α=0.3

                                                                                                                      59
                                                                                                                           UniCSE 1 (1), 55 -63, 2010

 and average of the results obtained are shown in figure 4.5. Set                                                                                             97
                                                                                                                                                              96
 of rules, the accuracy are summarizes in figure 4.5 with                                                                                                     95
                                                                                                                                                              94
                                                                                                                                                              93
 different value of fuzzy filter α.                                                                                                                           92
                                                                                                                                                              91
                                                                                                                                                              90




                                                                                                                                                 Accuracy
                                                  90                                                                                                          89
                                                                                                                                                              88
                                                  80                                                                                                          87
                                                                                                                                                              86
                                                  70                                                                                                          85
                               Numbers of rules




                                                                                                                                                              84
                                                  60                                                                                                          83
                                                  50                                                                                                          82
                                                                                                                                                              81
                                                  40                                                                                                          80
                                                                                                                                                              79
                                                  30                                                                                                          78
                                                  20
                                                                                                                                                                   0.5                            0.6             0.7                    0.8                  0.9             1
                                                  10                                                                                                                                                                   Th re sh ol d (β)
                                                      0                                                                                                                                                   AM            AMCL                   IG             IGCL

                                                      0.5         0.6               0.7             0.8                 0.9             1
                                                                         AM
                                                                                      Th re sh ol d (β)
                                                                                       AMCL                 IG          IGCL
                                                                                                                                                       Figure 4.5.f: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.3
                                                                                                                                                                                  60
                                                                                                                                                                                  55
      Figure 4.5.a: The number of rules for AM,AMCL,IG and IGCL with α = 0.1                                                                                                      50
                                                                                                                                                                                  45




                                                                                                                                                               Numbers of rules
                                              97
                                              96                                                                                                                                  40
                                              95
                                              94                                                                                                                                  35
                                              93                                                                                                                                  30
                                              92
                                              91                                                                                                                                  25
                                              90
                      Accuracy




                                              89                                                                                                                                  20
                                              88                                                                                                                                  15
                                              87
                                              86                                                                                                                                  10
                                              85
                                              84                                                                                                                                   5
                                              83
                                              82                                                                                                                                   0
                                              81
                                              80
                                              79
                                                                                                                                                                                    0.5             0.6                0.7                0.8                 0.9             1
                                              78                                                                                                                                                                            Thre shold (β)
                                                                                                                                                                                                           AM                AMCL              IG             IGCL
                                                      0.5     0.6               0.7              0.8               0.9              1
                                                                                     Thre shold (β)
                                                                        AM            AMCL             IG          IGCL                           Figure 4.5.g: The number of rules for AM,AMCL,IG and IGCL with α = 0.4
                                                                                                                                                              97
             Figure 4.5.b: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.1                                                                            96
                                                                                                                                                              95
                                             90                                                                                                               94
                                                                                                                                                              93
                                             80                                                                                                               92
                                                                                                                                                              91
                                                                                                                                                              90
                                                                                                                                                   Accuracy


                                             70
                                                                                                                                                              89
                     Numbers of rules




                                             60                                                                                                               88
                                                                                                                                                              87
                                             50                                                                                                               86
                                                                                                                                                              85
                                                                                                                                                              84
                                             40                                                                                                               83
                                                                                                                                                              82
                                             30                                                                                                               81
                                                                                                                                                              80
                                             20                                                                                                               79
                                                                                                                                                              78
                                             10
                                                  0                                                                                                                      0.5                      0.6                0.7                  0.8                  0.9                1
                                                                                                                                                                                                                        Thre shold (β)
                                                   0.5        0.6              0.7               0.8               0.9              1                                                                      AM                AMCL                   IG          IGCL
                                                                                     Thre shold (β)
                                                                        AM           AMCL              IG          IGCL                                       Figure 4.5.h: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.4
      Figure 4.5.c: The number of rules for AM,AMCL,IG and IGCL with α = 0.2                                                                                  100
                                                                                                                                                               90
                                   97
                                   96                                                                                                                          80
                                   95                                                                                                                          70
                                   94
                                   93                                                                                                                          60                                                                                         N. Rules
                                   92                                                                                                                          50
                                   91                                                                                                                          40                                                                                         Traning Accuracy
                                   90
              Accuracy




                                   89                                                                                                                          30                                                                                         Test Accuracy
                                   88                                                                                                                          20
                                   87
                                   86                                                                                                                                                     AM        AMCL               IG           IGCL
                                   85
                                   84
                                   83
                                   82
                                   81
                                   80
                                   79                                                                                                                         Figure 4.6: Accuracy of AMCL is higher and tree is smaller than other
                                   78                                                                                                                                                    algorithms.
                                                  0.5        0.6               0.7               0.8               0.9              1                         TABLE 4.4: NUMBERS OF RULES, TRAINING AND TESTING ACCURACY
                                                                                    Threshold (β)
                                                                                                                                                                                                                AM             AMCL                      IG            IGCL
                                                                        AM           AMCL              IG          IGCL
                                                                                                                                                                                       N. Rules                 58                  32                   59             35
             Figure 4.5.d: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.2
                                                                                                                                                               Training Accuracy                                95               95.3                    95             95
     Moreover, the comparison between IG, IGCL, AM and
 AMCL is shown in figure 4.6, which summarized in table 4.4,                                                                                                                      Test Accuracy                93.02            94.61                    94            94.1
 the size of tree by AMCL is smaller that the other.
                      60                                                                                                                         D. Dataset of Iris Problem
                      55
                      50                                                                                                                              This is Fisher's famous Iris data, which has been
                      45
                                                                                                                                                 extensively studied in the statistics and machine learning.
  Numbers of rules




                      40
                      35
                      30                                                                                                                         Number of instances is 150; numbers of attributes are four
                      25
                      20
                                                                                                                                                 attribute Information [8] :
                      15
                      10
                       5
                       0

                                        0.5                 0.6               0.7             0.8                0.9            1
                                                                                Thre shol d (β)
                                                                   AM           AMCL              IG             IGCL


Figure 4.5.e: The number of rules for AM, AMCL,IG and IGCL with α=0.3
                                                                                                                                            60
                                                                                                  UniCSE 1 (1), 55 -63, 2010
                                                                                                                                                   10
                        8
                                                                                                                                                           9
                        7
                                                                                                                                                           8
                        6




                                                                                                                          Numbers of rules
Numbers of rules




                                                                                                                                                           7
                        5
                                                                                                                                                           6
                        4
                                                                                                                                                           5
                        3                                                                                                                                  4
                        2                                                                                                                                  3
                        1                                                                                                                                  2
                        0                                                                                                                                  1
                               0.5        0.6               0.7             0.8          0.9           1                                                   0
                                                              Thre shold (β)
                                                  AM              AMCL         IG        IGCL                                                              0.5            0.6         0.7             0.8           0.9              1
                                                                                                                                                                                            Threshold (β)
Figure 4.8.a: The number of rules for AM,AMCL,IG and IGCL with α = 0.1                                                                                                           AM         AMCL            IG      IGCL

     1. Sepal length in cm                                                                                           Figure 4.8.e: The number of rules for AM,AMCL,IG and IGCL with α = 0.3
     2. Sepal width in cm                                                                                                Moreover, the comparison between IG, IGCL, AM and
     3. Petal length in cm                                                                                          AMCL is shown in figure 4.9, which summarized in table 4.6
     4. Petal width in cm                                                                                           the size of tree by AMCL is smaller than others.
     5.Class {Iris Setosa, Iris Versicolour, Iris Virginica}                                                                                          94


     70% of data for training and 30% for testing and average                                                                                         93


of the results obtained are shown in figure 4.8. Set of rules, the                                                                                    92




                                                                                                                             Accuracy
accuracy are summarizes in figure 4.8 with different value of                                                                                         91

fuzzy filter α.                                                                                                                                       90

                               94                                                                                                                     89


                               93                                                                                                                     88

                                                                                                                                                               0.5        0.6         0.7            0.8          0.9            1
                               92                                                                                                                                                       Thre shol d (β)
            Accuracy




                                                                                                                                                                                 AM     AMCL              IG      IGCL


                               91
                                                                                                                      Figure 4.8.f: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.3
                                                                                                                                                           10
                               90
                                                                                                                                                               9

                               89                                                                                                                              8
                                                                                                                                        Numbers of rules



                                                                                                                                                               7
                               88                                                                                                                              6
                                                                                                                                                               5
                                   0.5     0.6               0.7              0.8          0.9             1
                                                                   Thre shold (β)                                                                              4
                                                   AM              AMCL             IG     IGCL                                                                3
                                                                                                                                                               2
                        Figure 4.8.b: Accuracy of rules by AM,AMCL,IG and IGCL with α = 0.1                                                                    1
                               9                                                                                                                               0
                               8                                                                                                                                0.5        0.6        0.7            0.8          0.9            1
                               7                                                                                                                                                        Threshold (β)
                                                                                                                                                                                 AM         AMCL          IG      IGCL
            Numbers of rules




                               6
                               5
                                                                                                                     Figure 4.8.g: The number of rules for AM,AMCL,IG and IGCL with α = 0.4
                                                                                                                                             98
                               4
                                                                                                                                             97
                               3                                                                                                             96

                               2                                                                                                             95
                                                                                                                       Accuracy




                                                                                                                                             94
                               1
                                                                                                                                             93
                               0                                                                                                             92
                                                                                                                                             91
                                0.5        0.6               0.7             0.8           0.9             1                                 90
                                                                  Threshold (β)
                                                                                                                                             89
                                                   AM              AMCL             IG    IGCL
                                                                                                                                             88

             Figure 4.8.c: The number of rules for AM,AMCL,IG and IGCL with α = 0.2                                                                        0.5            0.6         0.7             0.8           0.9              1
                                                                                                                                                                                        Thre shold (β)
                                94
                                                                                                                                                                                 AM         AMCL            IG      IGCL

                                93
                                                                                                                     Figure 4.8.h: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.4
                                92
                   Accuracy




                                                                                                                       100
                                91                                                                                      90
                                                                                                                        80
                                90
                                                                                                                        70
                                                                                                                        60                                                                                       N. Rules
                                                                                                                        50
                                89                                                                                      40                                                                                       Traning Accuracy
                                                                                                                        30
                                88                                                                                      20                                                                                       Test Accuracy
                                                                                                                        10
                                    0.5     0.6              0.7              0.8          0.9          1                0
                                                                   Thre shold (β)
                                                       AM           AMCL            IG     IGCL                                                                      AM   AMCL     IG              IGCL
                                                                                                                                                                           Algorithms
                    Figure 4.8.d: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.2
                                                                                                                        Figure 4.9: Accuracy of AMCL is higher and tree is smaller than other
                                                                                                                                                   algorithms.




                                                                                                               61
                                                                                                     UniCSE 1 (1), 55 -63, 2010

                             Table 4.6: Numbers of rules, training and testing accuracy
                                                                                                                                                        92
                                                    AM                AMCL              IG              IGCL                                  91.5
                                                                                                                                                        91
                           N. Rules                 8                   4                9                6                                   90.5




                                                                                                                           Accuracy
                                                                                                                                                        90

  Training Accuracy                                91.9                92.6             91.2            92.4                                  89.5
                                                                                                                                                        89
                                                                                                                                              88.5
                     Test Accuracy                 95.2                96               96              96.4
                                                                                                                                                        88
                                                                                                                                              87.5

E. Pima Indians Diabetes Database                                                                                                                       87

                                                                                                                                                                 0.5         0.6              0.7              0.8            0.9           1
                                                                                                                                                                                                Th re sh ol d (β)
       This data catalogs the presence or absence of diabetes                                                                                                                       AM              AMCL            IG         IGCL


among Pima Indian females, the original source of the data is                                                            Figure 4.11.d: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.2
the National Institute of Diabetes, Digestive, and Kidney                                                                                     70

Disease (Indian), and it is available in UCI repository The                                                                                   60

training data has number of instances is 768 and number of




                                                                                                                           Numbers of rules
                                                                                                                                              50

Attributes is 8 plus class for each attribute (all numeric-value)                                                                             40

[8]:                                                                                                                                          30

     1. Number of times pregnant                                                                                                              20

     2. Plasma glucose concentration a2 hours in an oral                                                                                      10

        glucose tolerance test                                                                                                                    0

     3. Diastolic blood pressure (mm Hg)                                                                                                                 0.5                0.6               0.7             0.8
                                                                                                                                                                                                Thre shol d (β)
                                                                                                                                                                                                                              0.9           1

     4. Triceps skin fold thickness (mm)                                                                                                                                           AM           AMCL              IG          IGCL


     5. 2-hour serum insulin (mu .U/ml)                                                                                  Figure 4.11.e: The number of rules for AM,AMCL,IG and IGCL with α=0.3
     6. Body mass index (weight in kg/(height in m)^2)                                                                                                     89


     7. Diabetes pedigree function                                                                                                            88.5
     8. Age (years)                                                                                                         Accuracy
     9. Class variable (0 or 1) class 0 has 500 instances and                                                                                              88


        class 1 has 268 instances, 50% of data for training and                                                                               87.5
        50% for testing and average of the results obtained are
        shown in figure 4.11. Set of rules, the accuracy are                                                                                               87

                                                                                                                                                                 0.5          0.6               0.7               0.8            0.9                1
        summarizes in figure 4.11 with different value of fuzzy                                                                                                                                     Th re sh ol d (β)

        filter α.                                                                                                                                                                    AM               AMCL               IG          IGCL


                      80                                                                                                 Figure 4.11.f: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.3
                      70                                                                                                                                         80

                      60                                                                                                                                         70
   Numbers of rules




                      50                                                                                                                                         60
                                                                                                                                              Numbers of rules




                      40                                                                                                                                         50

                      30                                                                                                                                         40

                                                                                                                                                                 30
                      20
                                                                                                                                                                 20
                      10
                                                                                                                                                                 10
                       0
                                                                                                                                                                  0
                           0.5         0.6                0.7                 0.8              0.9             1
                                                              Thre shol d (β)                                                                                         0.5     0.6               0.7                 0.8              0.9            1
                                               AM               AMCL               IG         IGCL                                                                                                    Thre shol d (β)
                                                                                                                                                                                         AM           AMCL               IG      IGCL
 Figure 4.11.a: The number of rules for AM,AMCL,IG and IGCL with α=0.1
                       92                                                                                                Figure 4.11.g: The number of rules for AM,AMCL,IG and IGCL with α=0.4
                      91.5
                                                                                                                                                                 89
                       91
                      90.5
   Accuracy




                       90                                                                                                                              88.5
                      89.5
                                                                                                                                       Accuracy




                       89
                                                                                                                                                                 88
                      88.5
                       88
                                                                                                                                                       87.5
                      87.5
                       87
                                                                                                                                                                 87
                            0.5         0.6               0.7               0.8           0.9             1
                                                              Thre shol d (β)                                                                                     0.5         0.6               0.7              0.8            0.9             1
                                              AM               AMCL             IG           IGCL                                                                                                   Th re sh ol d (β)
                                                                                                                                                                                        AM           AMCL               IG      IGCL

 Figure 4.11.b: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.1
                      70                                                                                                Figure 4.11.h: Accuracy of rules by AM, AMCL, IG and IGCL with α = 0.4
                      60                                                                                                     Comparison between IG, IGCL, AM and AMCL is shown
                                                                                                                        in figure 4.12, which summarized in table 4.8 size of tree by
  Numbers of rules




                      50

                      40                                                                                                AMCL is smaller than others.
                      30

                      20

                      10

                       0

                       0.5            0.6               0.7              0.8             0.9             1
                                                           Thre shol d (β)
                                              AM              AMCL            IG         IGCL



  Figure 4.11.c:The number of rules for AM ,AMCL,IG and IGCL with
                                 α=0.2                                                                             62
                                                                  UniCSE 1 (1), 55 -63, 2010

       100
        90                                                                            [9]   Myung, K.L., M.L. Kyung, J.H. Lee and H.L. Hwang, "A fuzzy decision
        80                                                                                  trees induction method for fuzzy data ", IEEE International fuzzy
        70
        60                                                  N. Rules                        systems Conference proceedings, vol. 1 p.p. 16-21, August 1999.
        50
        40                                                  Traning Accuracy          [10] Quilnlan, J.R., "Induction of decision trees", Machine learning Vol. 1 pp.
        30                                                  Test Accuracy                   81-106, 1986.
        20
                AM      AMCL        IG         IGCL                                   [11] Tsang, E.C.C and D.S. Yeung, X.Z. Wang, "A comparative study on
                                                                                            heuristic algorithms for generating fuzzy decision trees". IEEE SMC ' 99
                                                                                            conference proceedings.IEEE International Conference on Systems,
                                                                                            Man. And Cybernetics, vol. 3. pp343 -348, 1999.
       Figure 4.12: Tree size of AMCL is smaller than other algorithms.
          Table 4.8: Numbers of rules, training and testing accuracy                  [12] Wang, T., Z. Li, Y. Yan, and H. Chen,” A Survey of Fuzzy Decision
                                                                                            Tree Classifier Methodology”, Fuzzy information and Engineering
                              AM         AMCL          IG          IGCL
                                                                                            (ICFIE), ASC 40, pp. 959–968, 2007.
          N. Rules            61          40           64              41             [13] Wang, X.Z. and H.M. Guang, "A comparison between fuzzy-ID3 and
          Training                                                                          OFFSS-Based fuzzy-ID3", Proceedings of 3rd International Conference
                             88.5        88.5         88.48            88.5
          Accuracy                                                                          on Machine Learning and Cybernetics, Shanghai, 2004.
        Test Accuracy        89.2        89.4         88.9             89.2           [14] Wang, X.Z., D.S. Yeung and E.C.C. Tsang, "Fuzzy rule mining by fuzzy
                                                                                            decision tree induction based on fuzzy feature subset", International
                            V.      CONCLUSION                                              Conference on Systems, Man, and Cybernetics, Tunisia, vol. 4, pp. 599 -
                                                                                            604, 2002.
    Tree induction has become an important technique for                              [15] Xue, L., H.Z. Xiao and D.Z.Dong “Four Matching Operators of Fuzzy
machine learning, expert system and prediction analysis and so                              Decision Tree Induction”, Proceedings of the Fourth International
on. Most existing methods are crisp and fuzzy decision tree                                 Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007)
induction. When choosing a decision tree induction method to                                vol.4, pages 674-678, 2007.
classify unseen instance, we mainly consider the generalization                       [16] Yeung, D.S., X.Z. Wang and E.C.C. Tsang, "A comparative study on
capability of tree induction. This paper analyzes and compares                              heuristic algorithms for generating fuzzy decision trees", IEEE
                                                                                            Transaction on systems, Man, and Cybernetics, Part B: Cybernetics, vol.
the generalization capability of decision tree between fuzzy and                            31, no.2, pp. 215-226, April 2001.
crisp tree algorithms. The initial conclusion is that, for the                        [17] Yeung, D.S., X.Z. Wang and E.C.C. Tsang, "Leaning weighted fuzzy
classification problem of numerical attributes; the fuzzy                                   rules from examples with mixed attributes by fuzzy decision trees",
decision tree has the stronger generalization capability than                               IEEE SMC'99 Conference Proceedings, IEEE International Conference
crisp one.                                                                                  on Systems, Man. And Cybernetics, vol. 3, pp343 -348, 1999.
    In this paper we presented a novel approach for evaluation                        [18] Yuan, Y. and M. J. Shaw, " Induction of fuzzy decision trees”, Fuzzy
the classifiability of instance based on evaluating the texture of                          Sets and systems, Vol. 69, pp.125-139, 1995.
class label surface. Based on that we also proposed an                                [19] Zhao, X.W., F. Chao and J. Sun, "Analysis on fuzzy filter in fuzzy
                                                                                            decision trees", Proceedings of 2nd International Conference on
algorithm for fuzzy decision tree induction using the                                       Machine Learning and Cybernetics.2-5 November, 2003.
classifiability of instance, the proposed method AMCL when                                                              AUTHORS PROFILE
combined Ambiguity heuristic with the CLassifiability of
                                                                                      Hesham Ahmed Hefny is an assistant professor and the head of Computer &
instance. More specifically, it results in smaller decision tree                      Information Sciences Department at the Institute of Statistical Studies and
and as a consequence better generalization (test) performance.                        research, Cairo University. His research interests include Artificial Neural
                                                                                      Networks, Fuzzy Systems, Genetic Algorithms, Swarm Intelligence, Pattern
                               REFERENCES                                             Recognition, and Data Mining. Dr. Hesham has published over 35 peer
                                                                                      refereed papers in academic journals and conferences on topics within
[1]   Dong, M. and R. Kothari, "Classifiability based pruning of decision
                                                                                      Artificial Intelligence and related areas.
      trees" IEEE Transactions on Fuzzy Systems, vol. 9, no.2, pp. 1739-1743,
      2001b.                                                                          Ahmed S. Ghiduk is an assistant professor at Beni-Suef University, Egypt.
                                                                                      He received the BSc degree from Cairo University, Egypt, in 1994, the MSc
[2]   Huang, Z. , T. D. Gedeon and M. Nikravesh, “Pattern Trees Induction: A
                                                                                      degree from Minia University, Egypt, in 2001, and a Ph.D. from Beni-Suef
      New Machine Learning Method”, IEEE Transactions on Fuzzy Systems,
                                                                                      University, Egypt in joint with College of Computing, Georgia Institute of
      vol. 16 no. 4, August 2008.
                                                                                      Technology, USA, in 2007. His research interests include software
[3]   Isao, H., "A formulation of learning type fuzzy ID3 ", available at:            engineering especially search-based software testing, genetic algorithms, and
      "http://www.cs.toronto.edu/~delue”, 2002.                                       ant colony. Currently, Ahmed S. Ghiduk is an assistant professor at College of
[4]   Juan, S., D.S. Yeung and X.Z. Wang, "An initial comparison of                   Computers and Information Systems, Taif University, Saudi Arabia.
      generalization capability between crisp and fuzzy decision trees",              Ashraf Abdelwahab is a professor of Computer Engineering, Electronics
      Proceedings of 1st International Conference on Machine Learning and             Research Institute, Cairo, Egypt. He received his M.Sc. in 1988, Faculty of
      Cybernetics, Bijing, 2004.                                                      Engineering, Cairo University in the area of Artificial Intelligence. In 1992 he
[5]   Kim, M.W., L.G. Joong and M. Changwoo, "Efficient rule generation               received his Ph.D. degree in Machine Learning and Evolutionary Algorithms.
      based on fuzzy decision tree for data mining ", IEEE International fuzzy        He has published over 150 technical papers in national and international
      systems Conference proceedings, vol. 1 p.p. 1223-1228, August 1999.             journals and conferences in the areas of Evolutionary Algorithms, Machine
[6]   Kothari, R. and M. Dong, "Lookahead based fuzzy decision tree                   Learning and Data Mining. Currently, Dr. Abdelwahab is Senior Advisor to
      induction", IEEE Transactions on Fuzzy Systems vol. 9, No.3, pp. 461-           the Minister of State for Administrative Development. He is responsible of
      468, 2001a.                                                                     developing, monitoring and coordinating E-government initiatives,
                                                                                      supervising the coordination with other ministries and international relations.
[7]   Liu, C.S., "Learning fuzzy rules from examples by fuzzy decision tree",
      available at: "http://neuron.et.ntust.edu.tw /m8802126", 2002.                  Mohamed Aboubaker is a Ph.D. student in Computer Sciences Department
                                                                                      at the Institute of Statistical Studies and Research, Cairo University. His Ph.D.
[8]   Merz, J.C. and P.M. Murphy UCI Repository of Machine Learning                   in the filed of decision tree. His research interests include rough and fuzzy set
      Database, available at: "ftp://ftp.ics.uci.edu/pub/machine-learning-            theory, pattern recognition, data mining, and knowledge discovery.
      database", 1996.




                                                                                 63

								
To top