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\title{An Evaluation of Data Mining Methods and Tools}
\author{Torgeir Dingsøyr \and Endre M. Lidal}

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\fancyhead[LE]{An Evaluation of Data Mining Methods and Tools}
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\samepage \begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|} \hline
Method & Description\\  \hline
Rough Sets & Founded on logic, statistics and algebra \\ 
Fuzzy Sets & Founded on logic and statistics \\ 
Bayesian Network & Founded on statistics\\ 
Neural Network & Black-box method \\ 
Decision Trees & Originates from machine learning \\  
Inductive log.prog. & Originates from machine learning, founded on
logic\\  \hline
\end{tabular}

\label{met1}
\end{center}
\end{table}
}

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[h]
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\samepage \begin{equation}P(Sure \; proposition) = 1
\end{equation}
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\end{equation}
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\samepage \begin{ex}% latex2html id marker 341
Consider the small information system, $\mathcal{A}=(U,A)$, illustrated
in Tab~\ref{table 1}.
\begin{table}
\begin{center}
\begin{tabular}[default]{c|c c c}
object & a & b & c   \\  \hline
1 & 1 & 2 & 3 \\  \hline
2 & 1 & 3 & 2 \\  \hline
3 & 1 & 2 & 3 \\  \hline
4 & 2 & 1 & 3 \\  \hline
5 & 2 & 1 & 3 \\  \hline
6 & 1 & 2 & 3 \\  \hline
7 & 1 & 3 & 3 \\  \hline
$\vdots$ & $\ldots$ & $\ldots$ & $\ldots$ \\ 
\end{tabular}
\caption{An information system}
\label{table 1}
\end{center}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}[default]{c|c c c c}
 & $E_{1}$ & $E_{2}$ & $E_{3}$ & $E_{4}$ \\  \hline
$E_{1}$ & $\emptyset$ &ab&bc&b \\ 
$E_{1}$ & ab & $\emptyset$ &abc&ab \\ 
$E_{1}$ & bc & abc & $\emptyset$ &c \\ 
$E_{1}$ & b & ab & c & $\emptyset$ \\ 
\end{tabular}
\caption{Discernibility matrix}
\label{tabel 3}
\end{center}
\end{table}
We see that some of the objects have the same value for all of the
attributes, for instance objects 1 and 6, and objects 4 and 5. These
objects are indiscernible by attributes \emph{a} through \emph{c}, and
theses objects are of the same \emph{equivalence
class}. Tab~\ref{tabel 2} illustrate the equivalence classes, the
attributes and the number of objects from the universe that are
indiscernible by attributes $a$ through $c$. The discernibility matrix
for $\mathcal{A}$ is shown in Tab~\ref{tabel 3}, and the reduct for
$\mathcal{A}$ is, RED(A)=\{b,c\}.
\begin{table}
\begin{center}
\begin{tabular}[default]{l|c c c|c}
Class & a & b & c &  \\  \hline
$E_{1}$ & 1 & 2 & 3 & 50 \\  \hline
$E_{2}$ & 2 & 1 & 3 & 11 \\  \hline
$E_{3}$ & 1 & 3 & 2 & 10 \\  \hline
$E_{4}$ & 1 & 3 & 3 & 19 \\  
\end{tabular}
\caption{Equivalence classes}
\label{tabel 2}
\end{center}
\end{table}
\end{ex}
}

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\samepage \begin{equation}% latex2html id marker 452
E_{i} \subseteq U/IND(A),\,there\,excists\,an\,X_{j} \subseteq
U/IND({d})\,such\,that E_{i} \subseteq X_{j}
\end{equation}
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{\newpage
\clearpage
\samepage \begin{ex}% latex2html id marker 463
Consider the decision system $\mathcal{A}=(U,A, \cup \{d\})$ as an extension
of the information system in Tab~\ref{tabel 2}, illustrate in
Tab~\ref{table 3}.
\begin{table}
\begin{center}
\begin{tabular}[default]{l|c c c|c|c}
Class & a & b & c & d &  \\  \hline
$E_{1}$ & 1 & 2 & 2 & 1 & 50 \\  \hline
$E_{2}$ & 2 & 3 & 2 & 2 & 30 \\  \hline
$E_{3}$ & 1 & 2 & 3 & 2 & 10 \\  \hline
$E_{4_{a}}$ & 2 & 1 & 3 & 2 & 9 \\  \hline
$E_{4_{b}}$ & 2 & 1 & 3 & 3 & 1 \\ 
\end{tabular}
\caption{A decision system}
\label{table 3}
\end{center}
\end{table}
We see that there is an inconsistency in class $E_{4}$, where 10 of the
objects have decision 2 and one object has decision 1.
\end{ex}
}

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\samepage \begin{ex}% latex2html id marker 503
We may get these definite rules from the decision system in Tab~\ref{table 3}:
\begin{itemize}
\item $E_{1}:a_{1}b_{2}c_{3} \rightarrow d_{1}$ 
\item $E_{2}:a_{2}b_{3}c{2} \rightarrow d_{2}$
\item $E_{3}:a_{2}b_{2}c{2} \rightarrow d_{2}$ 
\end{itemize}
Where $a_{1}$ denotes that $a=1$ and $b_{2}$ denotes that $b=2$, etc.
But for class $E_{4}$ we can not make rules that maps into exactly one
decision class.
\end{ex}
}

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{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\mu_{tr},\,0 \le \mu_{tr} \leq 1$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1863: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{equation}\mu(E,X)=\frac{|E \cap X|}{|E|} \geq \mu_{tr}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{ex}% latex2html id marker 537
Assume thresholds for decision system from Tab~\ref{table 3}:
\begin{itemize}
\item{$\mu_{tr}=1$ for $E_{4}$ we get no rules.}
\item{$\mu_{tr}=0.6$ for $E_{4}$ we get one rule:$E_{4}:a_{2}b_{1}c{3}
\rightarrow d_{2}$}
\item $\mu_{tr}=0.1$ for $E_{4}$ we get two rules: 
\begin{itemize}
\item{I:$E_{4}:a_{2}b_{1}c{3} \rightarrow d_{2}$ }
\item{II:$E_{4}:a_{2}b_{1}c{3} \rightarrow d_{3}$}
\end{itemize}
\end{itemize}
\end{ex}
}

{\newpage
\clearpage
\samepage \begin{ex}% latex2html id marker 566
Assume we want to classify a new object, with attributes:
$a_{2}b_{1}c_{2}$ and $d_{2}$. With the specialized rules from example
1.3 we can not make a match. If we glue together classes $E_{2}$ and
$E_{3}$ by removing attribute $b$ we get these new rules: 
\begin{itemize}
\item $E_{1}:a_{1}c_{3} \rightarrow d_{1}$ 
\item $E_{2},E_{3}:a_{2}c_{2} \rightarrow d_{2}$
\end{itemize}
We can now classify the object.
\end{ex}
}

\stepcounter{subsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\mu_{tr}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline1899: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}% latex2html id marker 644
\begin{center}
\footnotesize
\begin{verbatim}                                 CLASS = 0
Case #   FM_CODE                 (Cls  Prob)
-------------------------------------------------------------------------
   242   UST                           0.93
                                   3   0.07
   244   FTS                           1.00
   255   AIR                           1.00
   258   AIR                           1.00
   268   UST                           1.00
   271   UST                           1.00
   273   FTS                           1.00\end{verbatim}

\label{cnm}
\normalsize
\end{center}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}% latex2html id marker 652
\begin{center}
\footnotesize
\begin{verbatim} Case #  Class  Prob     Case #  Class  Prob     Case #  Class  Prob 
----------------------------------------------------------------------
      1    1    1.00         47    5    1.00         93    1    1.00
      2    2    1.00         48    1    1.00         94    0    1.00
      3    5    1.00         49    1    1.00         95    4    1.00
      4    5    1.00         50    3    1.00         96    0    1.00
      5    3    1.00         51    0    1.00         97    2    1.00\end{verbatim}

\label{mpc}
\normalsize
\end{center}
\end{figure}
}

\stepcounter{subsubsection}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}% latex2html id marker 668
\footnotesize
\begin{verbatim}attrib1 attrib2 attrib3 attrib4 attrib5 decision
string integer integer float(2) string string
Green 3 5 3.56 Round Ball
Red 56 5 4.78 Cubic Box
Cyan 3 5 2.64 Undefined Cone\end{verbatim}

\label{rif}
\normalsize
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[h]
\begin{center}
\scalebox{.5}{\includegraphics{rosetta-scr.gray.eps}}

\label{screenshot1}
\end{center}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 685
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|} \hline
 & & &Predicted& & \\  \hline 
 &Values&Decision1&Decision2&Decision3&Row Ratio \\  \hline
 &Decision1&119&12&71&0589109 \\  \hline
Actual&Decision2&29&184&48&0.704981 \\  \hline
 &Decision3&22&6&343&0.924528 \\  \hline
 &Column ratios&0.7&0.910891&0742424&0.77458 \\  \hline
\end{tabular}

\label{confex1}
\end{center}
\end{table}
}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 703
\scriptsize
\begin{center}
\begin{tabular}{|l|l|c|l|l|c|} \hline
Attribute&Description&Range&Attribute&Description&Range \\  \hline
EC\_CODE&equipment-code&16&SU\_CODE&sub-unit-code&33 \\   
FCAUSE\_CODE&failure-cause-code&20&SEVERITY&severity-code&4 \\ 
FD\_NO&failure-description&38&FC\_CODE&failure-consequence&13 \\ 
OM\_CODE&operating-mode&13&INST\_ID&installation-code&14 \\ 
I\_ID&inventory-index&162&MI\_CODE&maintenance-item&120 \\ 
IC\_CODE&installation\_category&4&OC\_CODE&operating\_category&3 \\ 
DC\_CODE&design\_class&30&SYS\_CODE&system-code&23 \\ 
OP\_CODE&operating-code&8&EE\_CODE&external-environment&5 \\ 
I\_NO\_OF\_STARTS&number of starts&33&I\_MANUFACT\_CTRL\_SYS&control
syst. manuf.&4  \\ 
I\_SUBSEA\_CS&subsea control system&1 &FM\_CODE&failure mode&42 \\  \hline
\end{tabular}

\label{attr1}
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\begin{center}
\begin{tabular}{|l|l|l|l|} \hline
Name&Objects&Attributes&Obj.w/miss val. \\  \hline
Experiment 1 & 3357 & 18& 1811 \\  \hline
\end{tabular}

\label{fact1}
\end{center}
\end{table}
}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
0 & -2.38e+01 & 0.201\\  \hline
1 & -2.47e+01 & 0.170\\  \hline
2 & -2.55e+01 & 0.155\\  \hline
3 & -2.41e+01 & 0.130\\  \hline
4 & -2.86e+01 & 0.107\\  \hline
5 & -2.25e+01 & 0.089\\  \hline
6 & -2.50e+01 & 0.083\\  \hline
7 & -1.84e+01 & 0.050\\  \hline
8 & -2.66e+01 & 0.015\\  \hline
\end{tabular}

\label{cl5}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|l|c|l|c|}      \hline
\emph{Attribute} & \emph{Influence} & \emph{Attribute} & \emph{Influence}\\  \hline
DC\_CODE       &   1.000 & SYS\_CODE       &   0.981\\  \hline
I\_ID     &   0.938 &EC\_CODE       &   0.935\\  \hline
INST\_ID       &   0.909 & I\_NUMBER\_OF\_STARTS      &   0.766\\  \hline
SU\_CODE       &   0.706 & MI\_CODE       &   0.690\\  \hline
OP\_CODE       &   0.525 & FCAUSE\_CODE       &   0.493\\  \hline
EE\_CODE       &   0.454 & OC\_CODE       &   0.387\\  \hline
FD\_NO       &   0.367 & FM\_CODE      &   0.353\\  \hline
IC\_CODE       &   0.312 & OM\_CODE       &   0.225\\  \hline
FC\_CODE       &   0.153 & SEVERITY       &   0.128\\  \hline
\end{tabular}

\label{ci5}
\normalsize
\end{center}
\end{table}
}

\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 761
\scriptsize
\begin{center}
\begin{tabular}{|l|l|c|l|l|c|} \hline
Gas Turbine&Description&Range&Electro Motors&Description&Range \\  \hline
SU\_CODE&sub-unit-code&6&INST\_ID&installation id&4\\   
FD\_NO&failure-description&34&FC\_CODE&failure-consequence&4\\ 
CLIMATE\_CODE&Climate&3&FD\_NO&failure-description&21\\ 
DC\_CODE&design\_class&2&MI\_CODE&maintenance-item&21 \\ 
SYS\_CODE&system-code&8&SU\_CODE&sub-unit-code&3\\ 
EE\_CODE&external-environment&3&CLIMATE\_CODE&Climate&2\\ 
I\_MODEL&model type&11&IC\_CODE&installation\_category&2\\ 
DRIVER\_APP&driver application&3&DC\_CODE&design\_class&1\\ 
POWER&model power&12&SYS\_CODE&system-code&5 \\ 
SPEED&speed design&12&OP\_CODE&operating-code&3\\ 
SHAFTS&\# of shafts&3&EE\_CODE&external-environment&2 \\ 
FUEL&fuel type&2&I\_MANUFACT&manufactor&6 \\ 
FM\_CODE&failure mode code&19&I\_MODEL&model type&11\\ 
INST\_ID&installation identifier&8&DRIVER\_APP&driver application&3\\ 
FC\_CODE&failure consequence&17&POWER&model power&11\\ 
MI\_CODE&maintenance-item&3&SPEED&speed design&6\\ 
OP\_CODE&operating-code&2&VARSPEED&variable speed&2\\ 
I\_MANUFACT&manufactor&12&VOLTAGE&voltage&6\\ 
I\_NO\_OF\_STARTS&number of starts&19&MOTOR&motor type&4\\ 
IC\_CODE&installation-category&3&SAFE&safety class&5 \\ 
 & & &FM\_CODE&failure mode&12 \\  \hline
\end{tabular}
\normalsize

\label{attr2}
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\begin{center}
\begin{tabular}{|l|c|c|c|} \hline
Name&objects&attributes&obj.w/miss.val.\\  \hline
Test set 2-GT&1198&20&641 \\ 
Test set 2-EM&67&21&48 \\  \hline
\end{tabular}

\label{fact2}
\end{center}
\end{table}
}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 783
\footnotesize
\begin{center}
\begin{tabular}{|l|l|c|c|c|c|} \hline
 &Reduct calc.& & &\multicolumn{2}{c|}{Overall result} \\ 
Test set&method&\# of reducts&\# rules&all rules&rules w/support$>$3 \\ 
\hline 
Training set w/&genetic obj.&  & & & \\ 
missing attributes&dynamic& 37 & 94 & 19\%& 23\% \\  \hline
Training set w/&genetic norm.&  & & & \\ 
missing attributes&non-dynamic&1 &17 & 17\%& N/A \\  \hline
Training set w/&Johnson obj.&  & & & \\ 
missing attributes&non-dynamic& 1 & 17 & 12.8\%& N/A \\  \hline
Training set no&genetic obj& & & & \\ 
missing attributes&dynamic& 36 & 90 & 19\%&21.2\% \\  \hline
\end{tabular}

\label{res2}
\end{center}
\normalsize
\end{table}
}

\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 804
\footnotesize
\begin{center}
\begin{tabular}{|c|l|c|c|c|c|} \hline
 &Type of& & &\multicolumn{2}{c|}{Overall result} \\ 
Test set no.&reducts&\# of reducts&\# of rules&all rules&rules
w/support$>$1 \\  \hline
 &genetic obj.& & & & \\ 
1&dynamic red.&208&2384&16\%&Not done \\  \hline
 &genetic obj.& & & & \\ 
2&dynamic red.&258&3406&54\%&46\% \\  \hline
 &genetic obj.& & & & \\ 
3&dynamic red.&139&1352&58\%&53\% \\  \hline
 &genetic obj.& & & & \\ 
4&dynamic red.&207&3014&47\%&48.3\% \\  \hline
 &genetic obj.& & & & \\ 
5&dynamic red.&212&2933&44\%&48.3\% \\  \hline
\end{tabular}

\label{res2b}
\end{center}
\normalsize
\end{table}
}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\footnotesize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
0 & -9.17e+00 & 0.284\\  \hline
1 & -1.73e+01 & 0.254\\  \hline
2 & -8.50e+00 & 0.254\\  \hline
3 & -1.17e+01 & 0.164\\  \hline
4 & -1.62e+01 &0.045\\  \hline
\end{tabular}

\label{cl7}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|l|c|l|c|}      \hline
\emph{Attribute} & \emph{Influence} & \emph{Attribute} & \emph{Influence}\\  \hline
POWER     &   1.000 & I\_MODEL   &   0.982\\  \hline
VOLTAGE   &   0.890 & I\_MANUFACT  &   0.826\\  \hline
SPEED     &   0.767 & SAFE      &   0.703\\  \hline
SYS\_CODE        &   0.643 & FD\_NO        &   0.561\\  \hline
MOTOR     &   0.549 & MI\_CODE   &   0.509\\  \hline
INST\_ID   &   0.462 & DRIVER\_APP &   0.435\\  \hline
FM\_CODE       &   0.398 & FCAUSE\_CODE        &   0.383\\  \hline
VARSPEED  &   0.290 & CLIMATE\_CODE &   0.230\\  \hline
EE\_CODE   &   0.230 & SU\_CODE   &   0.177\\  \hline
OP\_CODE   &   0.137 & IC\_CODE   &   0.026\\  \hline
DC\_CODE        &   0.000 & & \\  \hline
\end{tabular}

\label{ci7}
\normalsize
\end{center}
\end{table}
}

\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 854
\scriptsize
\begin{center}
\begin{tabular}{|l|l|c|} \hline
Attribute Gas Turbine&Description&Range\\  \hline
SU\_CODE&sub-unit-code&6\\ 
FD\_NO&failure-description&34\\ 
CLIMATE\_CODE&Climate&3\\ 
DC\_CODE&design\_class&2\\ 
SYS\_CODE&system-code&8\\ 
EE\_CODE&external-environment&3\\ 
I\_MODEL&model type&11\\ 
DRIVER\_APP&driver application&3\\ 
POWER&model power&12\\ 
SPEED&speed design&12\\ 
SHAFTS&\# of shafts&3\\ 
FUEL&fuel type&2\\ 
FM\_CODE&failure mode code&19\\ 
SEVERITY&severity&4\\  \hline
\end{tabular}
\end{center}

\label{attr3}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|l|c|} \hline
Decision& objects \\  \hline
C&378\\  \hline
D&290 \\  \hline
I&524 \\  \hline
\end{tabular}

\label{sevdist3}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|l|c|c|c|} \hline
Name&objects&attributes&obj.w/miss.val. \\  \hline
Test set 3-GT&1192&14&102 \\  \hline
\end{tabular}

\label{fact3}
\end{center}
\end{table}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|l|l|c|c|c|} \hline
Test set&Reducts type&\# of reducts&\# of rules&Overall res. \\  \hline
 &genetic obj& & & \\ 
20-80&dynamic red.&96&916&81.9\% \\  \hline
 &genetic obj& & & \\ 
30-70&dynamic red.&122&1248&77.5\% \\  \hline
 &genetic obj& & & \\ 
50-50&dynamic red.&157&1764&81.9\% \\  \hline
\end{tabular}

\label{res3a}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 902
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline
 & &\multicolumn{6}{c|}{Support} \\ 
Set&total&$>$2&$>$5&$>$10&$>$25&$>$40&$>$50 \\  \hline
Split 20-70\%&916&422&92&19&7&-&- \\  \hline
Split 30-80\%&1248&566&200&65&14&9&6 \\  \hline
Split 50-50\%&1764&958&360&125&29&10&7 \\  \hline
\end{tabular}

\label{left3-a}
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{figure}[h]
\begin{center}
\scalebox{.8}{\includegraphics{results1.eps}}

\label{ressup1}
\end{center}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|l|c|} \hline
Reducts&Support \\  \hline
\{FD\_NO\}&60 \\  \hline
\{SYS\_CODE, FM\_CODE\}&58\\  \hline
\{FD\_NO, SPEED\}&58\\  \hline
\{FM\_CODE\}&60\\  \hline
\{EE\_CODE, FM\_CODE\}&60\\  \hline
\{FD\_NO, FM\_CODE\}&60\\  \hline
\{SU\_CODE, FM\_CODE\}&60\\  \hline
\{FUEL, FM\_CODE\}&58\\  \hline
\{FD\_NO, I\_MODEL\}&60\\  \hline
\{POWER, FM\_CODE\}&60\\  \hline
\{I\_MODEL, FM\_CODE\}&60\\  \hline
\{FD\_NO, POWER\}&59\\  \hline
\{FD\_NO, SU\_CODE\}&60\\  \hline
\end{tabular}

\label{red3-a}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 934
\footnotesize
\begin{center}
\begin{tabular}{|l|c|} \hline
Rule&Support \\  \hline
SYS\_CODE(MP) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(I)&53\\  \hline
FM\_CODE(FTS) $\Rightarrow$ SEVERITY(C)&50\\  \hline
FM\_CODE(AIR) $\Rightarrow$ SEVERITY(I)&72\\  \hline
SU\_CODE(CM) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(I)&54\\  \hline
DRIVER\_APP(GENERATOR) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(I)&61\\  \hline
SHAFTS(2) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(I)&61\\  \hline
\end{tabular}

\label{rul3-a}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|c|c|c|c|c|} \hline
Values&D&C&I&Row ratios \\  \hline
D&110&22&70&0.544554\\  \hline
C&13&198&50&0.758621\\  \hline
I&23&6&342&0.921833\\  \hline
Column ratios&0.753425&0.876106&0.74026&0.779377\\  \hline
\end{tabular}

\label{conf3-a}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}\footnotesize
\begin{center}
\begin{tabular}{|l|l|c|c|c|} \hline
Test set&Reducts type&\# of reducts&\# of rules&Overall res. \\  \hline
 &genetic normal& & & \\ 
30-70&non-dynamic&1&259&38.3\% \\  \hline
 &genetic normal& & & \\ 
30-70&dynamic red.&25&5476&88.3\% \\  \hline
 &genetic obj& & & \\ 
30-70&dynamic red.&94&680&86.6\% \\  \hline
 &genetic normal& & & \\ 
20-80&non-dynamic&1&172&45.4\% \\  \hline
 &genetic normal& & & \\ 
20-80&dynamic red.&25&3265&90.3\% \\  \hline
 &genetic normal& & & \\ 
50-50&dynamic red.&23&7021&78.9\% \\  \hline
\end{tabular}

\label{res3-b}
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 976
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|} \hline
 & &\multicolumn{4}{c|}{Support} \\  
Set&total&$>$2&$>$5&$>$10&$>$25\\  \hline
Split 20-80\%&3265&1040&188&34&3 \\  \hline
Split 30-70\%&5476&1319&206&31&1 \\  \hline
\end{tabular}

\label{left3-b}
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{figure}[h]
\begin{center}
\scalebox{.8}{\includegraphics{results2.eps}}

\label{ressup2}
\end{center}
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{table}\begin{center}
\footnotesize
\begin{tabular}{|l|l|}\hline
Reducts&Support \\  \hline
\{FD\_NO, I\_MODEL, FUEL, FM\_CODE\}&6 \\  \hline
\{FD\_NO, POWER, FUEL, FM\_CODE\}&9\\  \hline
\{FD\_NO, FM\_CODE\}&7\\  \hline
\{SU\_CODE, POWER, FUEL, FM\_CODE\}&4\\  \hline
\{FD\_NO, FUEL, FM\_CODE\}&7\\  \hline
\end{tabular}

\label{red3-b}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1005
\begin{center}
\scriptsize
\begin{tabular}{|l|c|c|}\hline
Rules&Support \\  \hline
FD\_NO(30) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(O)&16\\  \hline
FD\_NO(10) AND FM\_CODE(FTS) $\Rightarrow$ SEVERITY(C)&14\\  \hline
FD\_NO(33) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(O)&12\\  \hline
SU\_CODE(CM) AND POWER(28000.00) AND FUEL(DUAL) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(O)&19\\  \hline
FD\_NO(10) AND FUEL(DUAL) AND FM\_CODE(FTS) $\Rightarrow$ SEVERITY(C)&13\\  \hline
SPEED(4930) AND FUEL(DUAL) AND FM\_CODE(AIR) $\Rightarrow$ SEVERITY(O)&19\\  \hline
SPEED(4930) AND FUEL(DUAL) AND FM\_CODE(UST) $\Rightarrow$ SEVERITY(C)&12\\  \hline
\end{tabular}

\label{rul3-b}
\end{center}
\normalsize
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1014
\begin{center}
\footnotesize
\begin{tabular}{|c|c|c|c|c|}\hline
Values&O&C&Undefined&Row ratios\\  \hline
O&620&5&22&0.958269\\  \hline
C&63&246&2&0.790997\\  \hline
Undefined&0&0&0&Undefined\\  \hline
Column ratios&0.90776&0.98008&0&0.903967\\  \hline
\end{tabular}

\label{conf3-b}
\end{center}
\normalsize
\end{table}
}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
0 &  -9.11e+00 & 0.286 \\  \hline
1 &  -8.10e+00 & 0.269\\  \hline
2 &  -9.43e+00 & 0.092\\  \hline
3 &  -8.86e+00 & 0.092\\  \hline
4 &  -1.45e+01 & 0.080\\  \hline
5 &  -1.43e+01 & 0.071\\  \hline
6 &  -7.98e+00 & 0.063\\  \hline
7 &  -9.60e+00 & 0.046\\  \hline
\end{tabular}

\label{cl0}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|l|c|c|c|c|}      \hline
\emph{Attribute} & \emph{20\%} & \emph{30\%} & \emph{50\%}& \emph{Two decisions\%}
\\  \hline
POWER     	& 1.000	& 1.000	& 1.000 & 1.000\\  \hline
I\_MODEL  	& 0.999	& 0.998	& 0.947 & 0.998\\  \hline
SPEED    	& 0.900	& 0.890	& 0.898 & 0.917\\  \hline
SYS\_CODE  		& 0.603 & 0.614	& 0.613 & 0.623\\  \hline
CLIMATE\_CODE  	& 0.411 & 0.347	& 0.299 & 0.355\\  \hline
DRIVER\_APP    	& 0.388	& 0.405 & 0.340 & 0.331\\  \hline
FD\_NO  		& 0.369	& 0.368	& 0.315 & 0.326 \\  \hline
EE\_CODE  	& 0.366	& 0.389	& 0.337 & 0.368 \\  \hline
DC\_CODE 		& 0.255	& 0.244	& 0.244 & 0.299 \\  \hline
FM\_CODE      	& 0.216	& 0.206	& 0.260 & 0.220  \\  \hline
FUEL     	& 0.203	& 0.206	& 0.194 & 0.172 \\  \hline
SHAFTS   	& 0.162	& 0.168	& 0.221 & 0.247 \\  \hline
SU\_CODE  	& 0.135	& 0.121	& 0.119 & 0.086  \\  \hline
SEVERITY  		& 0.034	& 0.034	& 0.099 & 0.049 \\  \hline
\end{tabular}

\label{ci0}
\normalsize
\end{center}
\end{table}
}

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{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
 0  &  -8.84e+00 & 0.299 \\  \hline
 1  &  -8.10e+00 & 0.243\\  \hline
 2  &  -9.23e+00 & 0.098 \\  \hline
 3  &  -1.28e+01 & 0.092 \\  \hline
 4  &  -9.83e+00 & 0.084 \\  \hline
 5  &  -1.32e+01 & 0.081 \\  \hline
 6  &  -7.98e+00 & 0.056 \\  \hline
 7  &  -1.45e+01 & 0.047 \\  \hline
\end{tabular}

\label{cl8}
\normalsize
\end{center}
\end{table}
}

\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
0 & -8.57e+00 & 0.248 \\  \hline
1 & -9.25e+00 & 0.194 \\  \hline
2 & -9.63e+00 & 0.114 \\  \hline
3 & -6.64e+00 & 0.101 \\  \hline
4 & -7.15e+00 & 0.070 \\  \hline
5 & -9.34e+00 & 0.064 \\  \hline
6 & -9.95e+00 & 0.064 \\  \hline
7 & -1.33e+01 & 0.055 \\  \hline
8 & -8.83e+00 & 0.034 \\  \hline
9 & -1.02e+01 & 0.032 \\  \hline
0 & -1.38e+01 & 0.023 \\  \hline
\end{tabular}

\label{cl9}
\normalsize
\end{center}
\end{table}
}

\stepcounter{subsubsection}
{\newpage
\clearpage
\samepage \begin{table}[h]
\begin{center}
\scriptsize
\begin{tabular}{|c|c|c|}      \hline
\emph{Class} & \emph{Strength} & \emph{Norm weight} \\  \hline
0 & -8.50e+00 & 0.276\\  \hline
1 & -8.20e+00 & 0.265\\  \hline
2 & -9.27e+00 & 0.120\\  \hline
3 & -8.35e+00 & 0.084\\  \hline
4 & -8.50e+00 & 0.067\\  \hline
5 & -1.37e+01 & 0.056\\  \hline
6 & -1.21e+01 & 0.050\\  \hline
7 & -9.32e+00 & 0.042\\  \hline
8 & -9.61e+00 & 0.042\\  \hline
\end{tabular}

\label{cl4}
\normalsize
\end{center}
\end{table}
}

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{\newpage
\clearpage
\samepage \begin{table}[!h]
\footnotesize
\begin{center}
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
AC& AC power \\ 
DC& DC power \\ 
AD& Aeroderivative \\ 
IN& Industrial \\  \hline
\end{tabular}

\label{dc}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1206
[!h]
\begin{center}
\scriptsize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
MODERATE&Partly closed and/or moderatly exposed. Manually ventilated. \\ 
LOW&Enclosed and/or indoor. Little exposed. Mechanically ventilated. \\ 
SEVERE&Not enclosed and/or outdoors. Hevily exposed (vibration, heat,
dust, salt) \\ 
UNKNOWN&Environmental exposure not known. \\  \hline
\end{tabular}

\label{ee}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1218
[!h]
\begin{center}
\scriptsize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
10&Mechanical failure - general \\ 
11&Leakage \\ 
12&Vibration \\ 
13&Clearance/allignment failure \\ 
14&Deformation \\ 
15&Looseness \\ 
16&Sticking \\ 
20&Material failure - general \\ 
22&Corrosion \\ 
24&Wear \\ 
25&Breakage \\ 
26&Fatigue \\ 
27&Overheat \\ 
28&Burst \\ 
30&Instrumental failure - general \\ 
31&Control failure \\ 
32&No signal/indication/alarm \\ 
33&Faulty signal/indication/alarm \\ 
34&Out of adjustment \\ 
35&Software failure \\ 
40&Electric failure - general \\ 
41&Short circuit \\ 
42&Open circuit \\ 
43&No power/voltage \\ 
44&Faulty power/voltage \\ 
45&Earth/isolation fault \\ 
50&External influence - general \\ 
51&Blockage/plugged \\ 
52&Contamination \\ 
53&Misc. external influences \\ 
90&Miscellaneous - general \\ 
91&No cause found\\ 
93&Other \\ 
94&Unknown \\  \hline
\end{tabular}
\caption[Description of the value codes for attribute 
\emph{Failure Description}] {Description of the value codes for
attribute \emph{Failure Description},
\emph{FD\_CODE}, which is a coded description of the failure.}
\label{fd}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1229
[!h]
\begin{center}
\scriptsize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
AIR&Abnormal instrument reading \\ 
BRD&Breakdown \\ 
ERO&Erratic output \\ 
ELF&External leakage - fuel \\ 
ELP&External leakage - process medium \\ 
ELU&External leakage - utility medium \\ 
FTS&Fail to start on demand \\ 
HIO&High output \\ 
INL&Internal leakage \\ 
LOO&Low output \\ 
NOI&Noise \\ 
OTH&Other \\ 
OHE&Overheating \\ 
PDE&Parameter deviation \\ 
SER&Minor in-service problem \\ 
STD&Structural deficiency \\ 
STP&Fail to stopp on demand \\ 
UNK&Unknown \\ 
UST&Spuriou stop \\ 
VIB&Vibration \\  \hline 
\end{tabular}

\label{fm}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1240
[!h]
\begin{center}
\footnotesize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
DUAL&Both diesel and gas \\ 
GAS&Gas \\  \hline
\end{tabular}
\caption[Description of the value codes for attribute \emph{Fuel}]
{Description of the value codes for attribute \emph{Fuel}, which
denotes the type of fuel the item uses.}
\label{fuel}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1250
[!h]
\begin{center}
\footnotesize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
C&Critical \\ 
D&Degraded \\ 
I&Incipient \\ 
U&Unknown \\  \hline
\end{tabular}
\caption[Description of the value codes for attribute \emph{Severity}]
{Description of the value codes for attribute \emph{Severity}, which
denotes the severity of the failure.}
\label{sev}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1260
[!h]
\begin{center}
\footnotesize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
CM&Control and monitoring \\ 
CS&Cooling system\\ 
EM&Electric motor\\ 
GG&Gas generator\\ \
LU&Lubrication system\\ 
MI&Miscellaneous\\ 
PO&Power turbine\\ 
ST&Starting system\\  \hline
\end{tabular}
\caption[Description of the value codes for attribute \emph{Sub Unit}]
{Description of the value codes for attribute \emph{Sub Unit},
\emph{SU\_CODE}, which gives a description of which part of the item that failed.}
\label{su}
\normalsize
\end{center}
\end{table}
}

{\newpage
\clearpage
\samepage \begin{table}% latex2html id marker 1271
[!h]
\begin{center}
\footnotesize
\begin{tabular}{|l|l|} \hline
Value&Description \\  \hline
CB&Combined function \\ 
EM&Emergency power \\ 
EP&Essential power \\ 
GE&Gas export \\ 
GP&Gas processing \\ 
GT&Gas treatment \\ 
MP&Main power \\ 
OH&Crude oil handling \\ 
WI&Water injection \\  \hline
\end{tabular}
\caption[Description of the value codes for attribute \emph{System}]
{Description of the value codes for attribute \emph{System},
\emph{SYS\_CODE}, which denotes the system that the item is a part of.}
\label{sy}
\normalsize
\end{center}
\end{table}
}

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\end{document}
