membershipEquations.tex

\documentclass{article}

\textheight 250mm
\textwidth 170mm
\hoffset -40mm
\voffset -25mm
\parindent 0mm

\def\If{\mbox{\bf~If~}}                   % "If" in the rules
\def\Then{\mbox{\bf~then~}}               % "then" in the rules
\def\Is{\mbox{~is~}}                      % "is" in the rules
\def\And{\mbox{\bf~and~}}                 % "and" in the rules
\def\Or{\mbox{\bf~or~}}                   % "or" in the rules
\def\Not{\mbox{\bf~not~}}                 % "not" in the rules
\newcommand{\lab}[1]{\mbox{\sc #1}}       % linguistic label
\newcommand{\var}[1]{\mbox{\em #1}}       % linguistic variable

\begin{document}

This model was generated on 22-12-2019 from 5403 data samples.
It has 4 inputs and 1 output. The sampling period is 1~s.
The termination tolerance of the clustering algorithm was 0.01,
and the random initial partition was generated with seed equal to 213256.
The output-specific parameters are given in the following table.


\begin{table}[htbp]
\centering
\caption{Model parameters.}
\begin{tabular}{|c|ccccc|}\hline
output & antecedent & $c$ & $m$ & $n_y$ & $n_u$ \\ \hline
1 & 1 & 3 & 2 & \{\{ [ ] \}, & \{\{ [ 0\, ] [ 0\, ] [ 0\, ] [ 0\, ] \}, \\
 &  &  &  & \{ [ ] \}\} & \{ [ 0\, ] [ 0\, ] [ 0\, ] [ 0\, ] \}\} \\ \hline
\end{tabular}
\label{tab:params}
\end{table}


In the following, the output-specific information is shown for each output.

Output1:


Rules:
$$
\begin{array}{l@{\hspace*{-0em}}l}
1. & \If u_1 \Is A_{11}\And u_2 \Is A_{12}\And u_3 \Is A_{13}\And u_4 \Is A_{14} \Then \\
   & \; y(k) = 2.7\cdot 10^{e-2}u_1-1.7\cdot 10^{e+8}u_2+6.2\cdot 10^{e-2}u_3-3.7\cdot 10^{e-1}u_4+4.0\cdot 10^{e-2} \\ \\
2. & \If u_1 \Is A_{21}\And u_2 \Is A_{22}\And u_3 \Is A_{23}\And u_4 \Is A_{24} \Then \\
   & \; y(k) = 5.0\cdot 10^{e-2}u_1-1.3\cdot 10^{e-2}u_2+9.3\cdot 10^{e-2}u_3+2.9\cdot 10^{e-1}u_4-5.1\cdot 10^{e-1} \\ \\
3. & \If u_1 \Is A_{31}\And u_2 \Is A_{32}\And u_3 \Is A_{33}\And u_4 \Is A_{34} \Then \\
   & \; y(k) = -1.1\cdot 10^{e-2}u_1+2.5\cdot 10^{e-3}u_2+8.1\cdot 10^{e-3}u_3-5.9\cdot 10^{e-1}u_4+1.3\cdot 10^{e+} \\ \\
\end{array}
$$


\begin{table}[htbp]
\centering
\caption{Consequent parameters.}
\begin{tabular}{|c|rrrrr|}\hline
rule & $u_1$ & $u_2$ & $u_3$ & $u_4$ &  offset \\ \hline
   1 & $2.7\cdot 10^{e-2}$ & $-1.7\cdot 10^{e+8}$ & $ 6.2\cdot 10^{e-2}$ & $-3.7\cdot 10^{e-1}$ & $ 4.0\cdot 10^{e-2}$ \\
   2 & $5.0\cdot 10^{e-2}$ & $-1.3\cdot 10^{e-2}$ & $ 9.3\cdot 10^{e-2}$ & $ 2.9\cdot 10^{e-1}$ & $-5.1\cdot 10^{e-1}$ \\
   3 & $-1.1\cdot 10^{e-2}$ & $ 2.5\cdot 10^{e-3}$ & $ 8.1\cdot 10^{e-3}$ & $-5.9\cdot 10^{e-1}$ & $ 1.3\cdot 10^{e+}$ \\
\hline
\end{tabular}
\label{tab:cons1}
\end{table}


\begin{table}[htbp]
\centering
\caption{Cluster centers.}
\begin{tabular}{|c|rrrr|}\hline
rule & $u_1$ & $u_2$ & $u_3$ & $u_4$ \\ \hline
   1 & $4.1\cdot 10^{e+}$ & $ 1.0\cdot 10^{e-19}$ & $ 2.4\cdot 10^{e+}$ & $ 2.0\cdot 10^{e-1}$ \\
   2 & $5.6\cdot 10^{e+}$ & $ 2.5\cdot 10^{e+}$ & $ 2.5\cdot 10^{e+}$ & $ 2.2\cdot 10^{e-1}$ \\
   3 & $2.3\cdot 10^{e+1}$ & $ 3.1\cdot 10^{e+}$ & $ 3.0\cdot 10^{e+}$ & $ 2.1\cdot 10^{e-1}$ \\
\hline
\end{tabular}
\label{tab:centers1}
\end{table}

\end{document}