=Paper=
{{Paper
|id=Vol-375/paper-2
|storemode=property
|title=ANN for prognosis of abdominal pain in childhood: use of fuzzy modelling for convergence estimation
|pdfUrl=https://ceur-ws.org/Vol-375/paper1.pdf
|volume=Vol-375
}}
==ANN for prognosis of abdominal pain in childhood: use of fuzzy modelling for convergence estimation==
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                         ANN for prognosis of abdominal pain
                         in childhood: use of fuzzy modelling
                              for convergence estimation
                                         George C. Anastassopoulos, Lazaros S. Iliadis

Abstract. This paper focuses in two parallel objectives. First it            decision rules can predict which children are at risk for
aims in presenting a series of Artificial Neural Network models              appendicitis (appendicitis is the most common surgical condition
that are capable of performing prognosis of abdominal pain in                of the abdomen). One such numerically based system is based on
childhood. Clinical medical data records have been gathered and              a 6-part scoring system: nausea (6 point), history of local RLQ
used towards this direction. Its second target is the presentation and       pain (2 point), migration of pain (1 point), difficulty walking (1
application of an innovative fuzzy algebraic model capable of                point), rebound tenderness / pain with percussion (2 point), and
evaluating Artificial Neural Networks’ performance [1]. This                 absolute neutrophil count of >6.75 x 10`3/μL (6 point). A score <5
model offers a flexible approach that uses fuzzy numbers, fuzzy              had a sensitivity of 96.3% with a negative predictive value of
sets and various fuzzy intensification and dilution techniques to            95.6% for AA.
perform assessment of neural models under different perspectives.               To date, all efforts to find clinical features or laboratory tests,
It also produces partial and overall evaluation indices. The                 either alone or in combination, that are able to diagnose
produced ANN models have proven to perform the classification                appendicitis with 100% sensitivity or specificity have proven
with significant success in the testing phase with first time seen           futile. Also, there is only one research work [4] in bibliography
data.                                                                        based on ANN that deals with the abdominal pain prognosis in
                                                                             childhood.
                                                                                The incidence of Acute Appendicitis (AA) is 4 cases per 1000
1 INTRODUCTION                                                               children. However appendicitis despite pediatric surgeons’ best
                                                                             efforts remains the most commonly misdiagnosed surgical
    The wide range of problems in which Artificial Neural
                                                                             condition. Although diagnosis and treatment have improved,
Networks can be used with promising results, is the reason of their
                                                                             appendicitis continues to cause significant morbidity and still
growth [2, 3]. Some of the fields that ANNs are used are: medical
                                                                             remains, although rarely, a cause of death. Appendicitis has a
systems [4-6], robotics [7], industry [8 – 11], image processing
                                                                             male-to-female ratio of 3:2 with a peak incidence between ages 12
[12], applied mathematics [13], financial analysis [14],
                                                                             and 18 years. The mean age in the pediatric population is 6-10
environmental risk modelling [15] and others.
                                                                             years. The lifetime risk is 8.6% for boys and 6.7% for girls.
    Prognosis is a medical term denoting an attempt of physician to
                                                                                The 15 factors that are used in the routine clinical practice for
accurately estimate how a patient's disease will progress, and
                                                                             the assessment of AA in childhood are: Sex, Age, Religion,
whether there is chance of recovery, based on an objective set of
                                                                             Demographic data, Duration of Pain, Vomitus, Diarrhea, Anorexia,
factors that represent that situation. The inference about prognosis
                                                                             Tenderness, Rebound, Leucocytosis, Neutrophilia, Urinalysis,
of a patient when presented with complex clinical and prognostic
                                                                             Temperature, Constipation. The sex (males), the age (peak of
information is a common problem, in clinical medicine. The
                                                                             appearance of A.A in children aged 9 to 13 years), and the religion
diagnosis of a disease is the outcome of combination of clinical
                                                                             (hygiene condition, feeding attitudes, genetic predisposition) were
and laboratorial examinations through medical techniques.
                                                                             in relation with a higher frequency for AA. Anorexia, vomitus,
    In this paper various ANN architectures using different learning
                                                                             diarrhea or constipation and a slight elevation of the temperature
rules, transfer functions and optimization algorithms have been
                                                                             (370 C - 380 C) were common manifestation of AA. Additionally,
tried. This research effort was motivated form the fact that reliable
                                                                             abdominal tenderness principally in the RLQ of the abdomen and
and seasonable detection of abdomen pain constitute attainments in
                                                                             the existence of the rebound sign, are strongly related with AA.
effective treatment of disease and avoidance of relapses. That is
                                                                             Leucocytosis (>10.800 K/μl) with neutrophilia (neutrophil count >
why the development of such an intelligent model that can
                                                                             75%) is considered to be a significant clue for AA. Urinalysis is
collaborate with the doctors will be very useful towards successful
                                                                             useful for detecting urinary tract disease, normal findings on
treatment of potential patients.
                                                                             urinalysis are of limited diagnostic value for appendicitis.
                                                                                The role of race, ethnicity, health insurance, education, access to
                                                                             healthcare, and economic status on the development and treatment
2 DIAGNOSTIC FACTORS OF ABDOMINAL                                            of appendicitis are widely debated. Cogent arguments have been
PAIN                                                                         made on both sides for and against the significance of each
Several reports have described clinical scoring systems                      socioeconomic or racial condition. A genetic predisposition
incorporating specific elements of the history, physical                     appears operative in some cases, particularly in children in whom
examination, and laboratory studies designed to improve diagnostic           appendicitis develops before age 6 years. Although the disorder is
accuracy of abdominal pain [16]. Nothing is guaranteed, but                  uncommon in infants and elderly, these groups have a
Democritus University of Thrace, Hellenic Open University                    disproportionate number of compilations because of delays in
anasta@med.duth.gr, liliadis@fmenr.duth.gr                                   diagnosis and the presence of comorbid conditions.




                                                                         1
   As diagnosis, there are four stages of appendicitis, including           (TanH) transfer function the input data were normalized (divided
acute focal appendicitis, acute supurative appendicitis, gangrenous         properly) in order to be included in the acceptable range of [-3, 3]
appendicitis and perforated appendicitis. These distinctions are            to avoid problems such as saturation, where an element’s
vague, and only the clinically relevant distinction of perforated           summation value (the sum of the inputs times the weights) exceeds
(gangrenous appendicitis includes into this entity as dead intestine        the acceptable network range [17]. Standard back-propagation
functionally acts as a perforation) versus non-perforated                   optimization algorithms using TanH, or Sigmoid or Digital Neural
appendicitis (acute focal and supurative appendicitis) should be            Network Architecture (DNNA) transfer functions, combined with
made.                                                                       the Extended Delta Bar Delta (ExtDBD) or with the Quick Prop
   The present study is based on data set that is obtained from the         learning rules [18, 19] were employed. The ExtDBD is a heuristic
Pediatric Surgery Clinical Information System of the University             technique reinforcing good general trends and damping oscillations
Hospital of Alexandroupolis, Greece. It consisted of 516 children’s         [20].
medical records. Some of these children had different stages of                Modular and radial basis function (RBF) ANN applying the
appendicitis and, therefore, underwent operative treatment. This            ExtDBD learning rule and the TanH transfer function were also
data set was divided into a set of 422 records and another set of 94        used in an effort to determine the optimal networks. RBFs have an
records. The former was used for training of the ANN, while the             internal representation of hidden neurons which are radially
latter for testing. A small number of data records were used as a           symmetric, and the hidden layer consists of pattern units fully
validation set during training to avoid overfitting. Table 1                connected to a linear output layer [21, 22].
represents the stages of appendicitis as well as the corresponding
cases for each one. The 3rd column of Table 1 depicts the coding
of possible diagnosis, as they used for ANN training and testing            3.2 ANN evaluation metrics applied
stages.
                                                                            Traditional ANN evaluation measures like the Root Mean Square
           Table 1. Possible diagnosis and corresponding cases.             Error (RMS error), R2 and the confusion matrix were used to
                    Diagnosis                    Coding      Cases          validate the ensuing neural network models. It is well known that
                  Discharge                         -2         236
                                                                            the RMS error adds up the squares of the errors for each neuron in
       Normal                                                               the output layer, divides by the number of neurons in the output
                  Observation                       -1         186
                  No findings                       0           15
                                                                            layer to obtain an average, and then takes the square root of that
                                                                            average. The confusion matrix is a graphical way of measuring the
         Operative




                  Focal appendicitis                 1          34
         treatment




                  Phlegmonous              or                               network’s performance during the “training” and “testing” phases.
                                                    2           29          It also facilitates the correlation of the network output to the actual
                 Supurative appendicitis
                  Gangrenous appendicitis            3           8          observed values that belong to the testing set in a visual display
                  Peritonitis                        4           8          [17], and therefore provides a visual indication of the network’s
                                                                            performance. A network with the optimal configuration should
                                                                            have the “bins” (the cells in each matrix) on the diagonal from the
3 NEURAL NETWORK DESIGN                                                     lower left to the upper right of the output. An important aspect of
                                                                            the matrix is that the value of the vertical axis in the generated
Data were divided into two groups, the training cases (TRAC) and            histogram is the Common Mean Correlation (CMC) coefficient of
the testing cases (TESC). The TRAC consisted of 417 concrete                the desired (d), and the actual (predicted) output (y) across the
medical data records and the TESC consisted of 101. Each input              Epoch.
record was organised in a format of fifteen fields, namely sex, age,           Finally, the FUSETRESYS (Fuzzy Set Transformer Evaluation
religion, area of residence, pain time period, vomit symptoms,              System) that constitutes an innovative ANN evaluation system has
diarrhoea, anorexia, located sensitivity, rebound, wbc, poly,               been applied offering a more flexible approach [1].
general analysis of urine, body temperature, constipation. The
output record contained a single field which corresponded to the
potential outcome of each case.                                             3.3 Technical description of the FUSETRESYS
    The determination if the TRAC and TESC data sets was
performed in a rather random manner. The training and testing
                                                                            ANN evaluation model
sample size which would be sufficient for a good generalization             Fuzzy logic enables the performance of calculations with
was determined by using the Widrow’s rule of thumb for the LMS              mathematically defined words called “Linguistics” [1, 23-25].
algorithm which is a distribution free, worst case formula [2] and it       FUSETRESYS faces each training/testing example as a Fuzzy Set.
is shown in the following equation 1. W is the total number of free         It applies triangular or trapezoidal membership functions in order
parameters in the network (synaptic weights and biases) and ε               to determine the partial degree of convergence (PADECOV) of the
denotes the fraction of the classification errors permitted during          ANN for each training/testing example separately. The following
testing. The O notation shows the order of quantity enclosed within         equations 2 and 3 represent a triangular and a trapezoidal
[2].                        ⎛W ⎞                       (1)                  membership functions respectively [1].
                       N = O⎜ ⎟
                            ⎝ε ⎠                                                  μs(x;a,b,c)=max{min{
                                                                                                          x − a c − x },0} a<b<c         (2)
                                                                                                               ,
   In the case examined here with 417 training examples used, the                                         b−a c−b
classification error that could be tolerated would be about 4%.
                                                                              μs(x;a,b,c,d)= max{min{ x − a ,1, d − x },0}a<b<c<d              (3)
                                                                                                         b−a    d −c
3.1 Description of the experiments performed                                The model can produce various overall degrees of convergence
   During experimentations, numerous ANN architectures,                     (OVDECOV) for all of the training examples by applying either
learning algorithms and transfer functions were combined in an              fuzzy T-Norm or fuzzy S-Norm conjunction operations, depending
effort to obtain the optimal network. For the Tangent Hyperbolic            on the optimistic or pessimistic point of view of the developer. T-

                                                                        2
Norms tend to produce lower aggregation indices so in the case of                                          performing weights are kept: one copy for training and another one
ANN evaluation they can be considered as a pessimistic approach,                                           of the best performing weights thus far.
whereas the opposite happens with S-Norms [26]. In fact, each
distinct Norm evaluates the performance of an ANN under a                                                           Table 2. Structure of the four most successful ML ANN
different perspective. For example the drastic product assigns the                                                                       Hidden         Second
ANN a high OVDECOV only if it does not have extreme                                                          Optimization      Input       sub-         Hidden
                                                                                                                                                                       Learning
deviations between the desired and the produced classifications                                                                                                      Rule/Transfer
                                                                                                              algorithm        Layer      layer           sub-
                                                                                                                                                                       Function
during the training/testing process [1] whereas the Einstein T-                                                                          neurons         layer
Norm acts in a more average mode. The following equations 4 and
5 present the drastic product and the Einstein product T-Norms.                                              ANN ML#1.
                                                                                                                                                                        Genetic
More details on fuzzy conjunction operators can be found in [26-                                             Reinforcement
                                                                                                                                   15        7             7           Algorithm
                                                                                                              ANN using
28].                                                                                                                                                                    /TanH
                                                                                                            BackPropagation
μ ⎛~ ~⎞
         = Min {μ ~ (Χ), μ ~ ( Χ)} if Max {μ ~ (Χ), μ ~ ( Χ)} = 1 else
  ⎜⎜ A ∩ B ⎟⎟           A           B                             A         B                                ANN ML#2.                                                  Norm-
   ⎝        ⎠
                                                                                                              Multilayer           15        9             0          Cum_Delta/
                                                                                                            Backpropagation                                             TanH
μ⎛              = 0 (4) ⎛⎜      ~
                                        ⎞                  μ {X )μ ( X )                         (5)
                        μ ⎜ Α ∩ Β ⎟⎟ =
     ~ ~⎞                           ~                         ~        ~
                                                              A        B
  ⎜⎜ A∩B ⎟⎟                                                                                                  ANN ML#3.                                                  Norm-
   ⎝      ⎠                 ⎜           ⎟   2 − [ μ ~ { X ) + μ ~ ( X ) − μ ~ { X ) μ ~ ( X )]
                            ⎝           ⎠           A             B         A         B                       Multilayer           15        9             9          Cum_Delta/
                                                                                                            Backpropagation                                             TanH
   The fact that the FUSETRESYS evaluates each training/testing
example separately, offers a more clear view of the ANN’s                                                    ANN ML#4.
                                                                                                                                                                       ExtDBD/
performance. In this way the developers know if the network                                                   Multilayer           15        7             0
                                                                                                                                                                        TanH
operates extremely bad or well in specific cases.                                                           Backpropagation
   Also when there are several neurons in the output layer, the
traditional approaches produce separate evaluation results for each                                        Table 3 shows the architecture and structure of the four most
one whereas the FUSETRESYS can produce an additive                                                         successful radial basis function (RBF) ANN.
performance index (ADPERI) of the ANN. This could be done
under different perspectives and under different degrees of
                                                                                                                   Table 3. Structure of the two most successful RBF ANN
optimism [1].
                                                                                                                                               Number
   Finally the application of fuzzy set hedges offers the “dilution”                                                                               of                  Learning
and the “intensification” options. In this way by using the dilution                                        Optimization Input                             Output
                                                                                                                                      Proto neurons                  Rule/Transfer
approach the developer softens the membership function over the                                              algorithm      Layer                           Layer
                                                                                                                                                Hidden                 function
fuzzy set and weakens the membership constraints so that a point                                                                                 layer
of the Universe of discourse is “truer” than it would be before [1,
27]. On the contrary the intensification hardens the MF over the FS                                           ANN 5.                                                        Norm
                                                                                                            ANN6 Radial                                                   Cum_Delta /
and strengthens the membership constraints so that a point on the                                                             15        30          2            1
domain is “less true” than it used to be [1, 27]. The following                                                Basis
                                                                                                             Function                                                     Sigmoid or
equations 6 and 7 correspond to the intensification and dilution                                                                                                             TanH
functions respectively.
μint ensify ( A) ( X i ) = μ An ( X i ) (6) μ dilute ( A ) ( X i ) = μ An ( X i )
                                                                                1
                                                                                           (7)                The following Table 4 presents the training and testing results
                                                                                                           for the most successful ML and RBF ANN using R2. Also for the
  In this way the ANN can be evaluated strictly by using a “very                                           three most successful networks, namely 2,3,4 the FUSETRESYS
well fit” evaluation option, or in a more relaxed way by using the                                         model was applied to determine the average degree of
“somewhat fit” option. Of course it is in the developer’s hand to                                          convergence. According to the results, the most suitable network
decide the potential type of the ANN’s evaluation and the degree                                           was ML#3. The structure and the architecture of this successful
of dilution or intensification. For a more detailed description of                                         network have been described in the above Table 2.
FUSETRESYS please see [1].                                                                                      Table 4. Evaluation of the most successful ML and RBF ANN
                                                                                                                                                                 Average Degree
                                                                                                                                                                  of success in
4 RESULTS AND DISCUSSION                                                                                     ANN                                  R2 in           Testing using
                                                                                                                       R2 in Training
4.1 ANN analysis                                                                                             code                                Testing         FUSETRESYS
                                                                                                                                                                  for the three
Several experiments were performed. The following table 2                                                                                                           best ANN
presents the structure of the four most effective Back Propagation                                              1           0.8258               0.8247
(BP) multilayer (ML) neural networks. In all cases of ANN                                                       2           0.9615               0.9471                0.9699
models, the classical approach for overcoming the overfitting                                                   3           0.9721               0.9489                0.9716
problem has been followed. More specifically, a set of validation                                               4           0.9352               0.9588                0.9799
data have been provided to the algorithm in addition to the training                                            5           0.9114               0.9000
data. The algorithm has monitored the error with respect to this                                                6           0.9346               0.9400
validation set, while using the training set to drive the gradient
descent search. The number of weight tuning iterations performed                                             The following figure 1 is a graphical representation of the all the
by the system, were determined in each case based on the criterion                                         PADECOV of the ML#2, for each testing example. The absolute
of lowest error over the validation set. Two copies of the best                                            degree of convergence has the value of one. A serious effort was

                                                                                                       3
made towards the development of modular ANN (MODANN) for
the classification problem solution. The term MODANN refers to
the “adaptive” mixtures of local experts (LOCEXP) as proposed
by [29].
  They consist of a group of BP ANN referred to as local experts
competing to learn different aspects of a problem. A “gating ANN”                                                                       Figure 2. Gating Probabilities of the MODANN with code #1Ref.
controls the competition and learns to assign different parts of the
data space to different networks.                                                                                                               Table 6. Small sample of the PADECOV indices
                                                                                                                                                        PADECOV by FUSETRESYS
    Fuzzy set "ANN output equal




                                  1.2
                                                                                                                                                        ML#2            ML#3        #1REF
     Membership values to the




                                   1
         to the right class"




                                  0.8
                                                                                                                                                       0.83333         0.83333         1
                                  0.6
                                  0.4                                                                                                                  0.83333         0.83333       0.833
                                  0.2
                                   0
                                                                                                                                                          1               1            1
                                        1   7   13   19   25   31   37   43   49    55   61   67       73   79   85   91   97
                                                                                                                                                       0.83333         0.83333         1
                                                               Code number for each evaluated record
                                                                                                                                                          1               1            1
                                                                                                                                                       0.83333         0.83333         1
  Figure 1. Representation of all the PADECOV of the network ML# 2
                                                                                                                                                      0.833333        0.833333         1
The LOCEXP have the same architecture but they can apply
distinct learning rules or transfer functions. Also the number of the                                                                                         OVDECOV Einstein
output processing elements of the gating network is equal to the
number of LOCEXP used. The number of the neurons in the                                                                                                0.98299         0.97784       0.971
hidden layer of the gating network should be larger than the
number of the output processing elements [17].                                                                                      The above Table 6 presents a small sample of the 101 distinct
                                                                                                                                    PADECOV values produced by the FUSTRESYS.
  Table 5. Refereed Back Propagation using Gating Networks with two                                                                   Also the Einstein T-Norm was applied for the determination of
                       Competing local experts                                                                                      the overall degree of convergence of the ANN. The ML#2 ANN
                                                                                                                                    had a very high OVEDECOV index with a value of 0.98299
 Refereed #1 REF ANN using Gating ANN with 2 Local Experts
                                                                                                                                    whereas the other ML#3 ANN and the MODANN #REF1 had
 Learning                                                                                                                           OVEDECOV indices as high as 0.97. The Drastic Product T-Norm
   rule                                 Transfer                 Error                   Output                   Noise             was not applied in this research effort because it was proven
                                                Local Expert's #1 functions                                                         unnecessary from the data in table 5 where there were no serious
                                                                                                                                    indications of extreme bad ANN performance in any of the testing
  ExtDBD                                    TanH               standard                  Direct                  Uniform            examples.
                                                Local Expert's #2 functions
   Norm-                                                                                                                            Table 7. OVDECOV values when intensification and dilution of first order
   Cum                                      TanH               standard                  Direct                  Uniform             was applied using Einstein product and Triangular membership function
   Delta                                                                                                                                              OVDECOV of          OVDECOV of       OVDECOV of
                                                                                                                                                           ML #2             #1REF             ML # 3
                                                Local Expert's Architecture                                                             Dilution
                                                                                                                                                          0.99972            0.99934           0.99957
   Input                                                       Hidden                                            Output               “Partly fit”
  neurons                                                      neurons                                           neurons            Intensification
                                                                                                                                                          0.75932            0.64887           0.71033
     15                                                           6                                                1                “Very well fit”

                                                     Gating ANN functions
 Learning                                                                                                                           5 CONCLUSIONS
   rule                                 Transfer                 Error                   Output                   Noise
                                                                                                                                    The above research has obtained six ANNs with good level of
  ExtDBD                                    Linear             Standard                  SoftMax                 Uniform            convergence and it has proven that there exist at least four ANNs
                                                                                                                                    that have high performance indices, in the case of abdominal pain
The above table 5 presents the structure and the architecture of the                                                                classification. Namely the best ANNs are two ML BP ANN, a RBF
optimal MODANN that was developed for the medical                                                                                   ANN and a MODANN using a referee gating network and two
classification problem examined here. The performance of the                                                                        local experts. All of them have been described in the previous
developed modular network is very satisfying, having an R2 value                                                                    sections.
of 0.9434 and a FUSETRESYS produced average PADECOV                                                                                    A very interesting part of the whole research effort is the
equal to 0.9733 (using the Triangular membership function) in the                                                                   application of an innovative ANN evaluation model called
testing process using the first time seen testing data set.                                                                         FUSETRESYS that uses fuzzy logic and fuzzy algebra proposed in
   The following figure 2 depicts the gating probabilities for the                                                                  [11].
optimal MODANN..                                                                                                                       The new evaluation scheme has performed individual
                                                                                                                                    convergence indices namely PADECOV, for the output of each
                                                                                                                                    single data record used in the testing phase. The worst PADECOV
                                                                                                                                    value equals to 0.6666 which actually is the degree of membership
                                                                                                                                    of each data record to the FS “Actual output value equal to the
                                                                                                                                    desired value”. This worst case appears three times exactly in the

                                                                                                                                4
same cases of data records, for the ML#2, ML#3, #1REF ANN and                        [7]  V. Rankovic and I. Nikolic, ‘Control of industrial Robot using neural
it shows that the classification capacity of the developed networks                       network compensator’, Theoretical Applications of Mech., 32, No. 2,
is not bad even in the worst cases. This conclusion becomes                               147-163, (2005).
                                                                                     [8] S. Avramidis and L. Iliadis, ‘Wood-water sorption isotherm
stronger by considering the fact that the second worst PADECOV
                                                                                          prediction with artificial neural networks: a preliminary study’,
index has a value of 0.833.                                                               Holzforschung, 59, 336 – 341, (2005).
   If an overall ANN validation is performed the traditional                         [9] S. Mansfield, L. Iliadis, S. Avramidis, ‘Neural Network Prediction of
evaluation instruments agree with the FUSETRESYS that the most                            Bending Strength and Stiffness in Western Hemlock’,
suitable ANN is the ML BP with code# 4 whereas all of the other                           HOLZFORSCHUNG, 61, Issue 6, 707-716 Walter De Gruyter & Co
developed ANN have almost an equally good performance. The                                Berlin, New York, 2007.
Einstein T-Norm produces a higher “good performance index” for                       [10] B. Cannas, A. Fanni, A. Montisci, G. Murgia and P. Sonato,
the MODANN than the traditional methods.                                                  ‘Dynamic Neural Networks for Prediction of Disruptions in
                                                                                          Tokamaks’, Proceedings of the 10th International Conference on
   As it can be seen in table 7, the OVDECOV indices have very
                                                                                          Engineering Applications of Neural Networks (EANN), Thessaloniki,
high values for ML#2 and for REF#1 and ML#3 networks when a                               Greece. 2007.
“Partly fit” validation is performed. There is significant                           [11] L. Iliadis, S. Spartalis and S. Tachos, ‘A Fuzzy intelligent Artificial
differentiation when a very strict evaluation is done under the                           Neural Network evaluation System: Application in Industry’,
linguistic “Very well fit”. The OVDECOV indices fall from 0.99                            Proceedings of the 10th International Conference Engineering
to 0.75 for ML#2, from 0.99 to 0.65 for #REF and from 0.99 to                             Applications of Neural Networks, 320-326, Thessaloniki, Greece,
0.71 for ML#3 respectively. This is a very useful approach and it                         2007.
shows the actual power of FUSETRESYS due to the fact that it                         [12] R. Kuhn, R. Bordas, B. Wunderlich, B. Michaelis and D. Thevenin,
                                                                                          ‘Colour class identification of tracers using artificial neural networks’,
shows the differentiation of the average convergence degree of the
                                                                                          Proceedings of the 10th International Conference on Engineering
three ANN when more strict validation methods are applied. So                             Applications of Neural Networks (EANN), Thessaloniki, Greece,
ANN fed with the same data records in testing and appearing to                            2007.
have more or less the same performance, they are very seriously                      [13] L. Iliadis and S. Spartalis, ‘Artificial Neural Networks equivalent to
differentiated when more strict convergence validation methods are                        Fuzzy Algebra T_Norm conjunction operators’, Proceedings (Book of
performed.                                                                                extended abstracts) of the ICCMSE 2007 Published by the AIP
   The proposed ANN architecture faces the appendicitis prediction                        (American Institute of Physics), USA, 2007.
quite satisfactory, based on both the above presented results, and                   [14] P. Hajek and V. Olej, ‘Municipal creditworthiness Modelling by
                                                                                          clustering methods’, Proceedings of the 10th International
the pediatric surgeon’s opinion that used these ANNs in their
                                                                                          Conference on Engineering Applications of Neural Networks (EANN),
everyday routine clinical practice.                                                       Thessaloniki, Greece, 2007.
   The innovative ANN evaluation model that was applied                              [15] L. Iliadis, ‘A decision support system applying an integrated Fuzzy
successfully in this research effort will be used extensively in the                      model for long - term forest fire risk estimation’, Environmental
future, in an integrated effort to check its validity under various                       Modelling and Software, 20, Issue 5, 613-621, (2005).
perspectives.                                                                        [16] M. Blazadonakis, V. Moustakis, and G. Charissis, ‘Deep Assessment
                                                                                          of Machine Learning Techniques Using Patient Treatment in Acute
                                                                                          Abdominal Pain in Children’, Artificial Intelligence in Medicine, 8,
ACKNOWLEDGEMENTS                                                                          527- 542, (1996).
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We would like to thank the pediatric surgeons of the Pediatric                            II/PLUS, Carnegie, PA,USA, 2001.
Surgeon Department of Medical School of Democritus University                        [18] R.A. Jacobs, ‘Increased rates of convergence through learning rate
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of Thrace, for their contribution in the concession of the medical
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