Re: Looking for book info


Subject: Re: Looking for book info
From: Jonathan G. Campbell (jg.campbell@qub.ac.uk)
Date: Thu Jun 22 2000 - 12:40:27 MET DST


Mikkel Holmen Andersen wrote:
>
> I read in this newsgroup that the book by Li-Xin Wang "Adaptive Fuzzy
> Systems and Control, Design and Stability Analysis" had a chapter about
> generating fuzzy rules from numerical data. However this book is no longer
> in print at the publisher.
>
> Does anybody know whether the "A Course in Fuzzy Systems and Control" by
> Li-Xin Wang includes anything about using numerical data for rule
> generation.
>

AFAIK the fuzzy-rules-from-numerical-data algorithm given in Li-Xin
Wang's book is identical to that in

@article{wang-mendel92a,
        AUTHOR = "L-X. Wang and J.M. Mendel",
        TITLE = "{Generating Fuzzy Rules by Learning
      from Examples}",
        JOURNAL = IEEE Trans. SMC,
        VOLUME = "22",
        YEAR = "1992",
        NUMBER = "6",
        MONTH = "November/December"}

So, maybe access the algorithm via that. Or, if you can disentangle the
following horrible LaTeX, it gives my version of the same.

\begin{figure}

{\bf Procedure: Wang-Mendel Training}

Input: Training data, $\mathbf{X_T} = \{ \mathbf{x}_n, y_n\}_{n=1}^N;$\\
Output: Fuzzy rule-base, $\mathbf{R} = \{r_k\}_{k=1}^K,\ r_k\ =\
(c_k,d_k);$

\begin{tabbing}
\=1234\=5678x\=9abc\=defg\=hijk\=lmno\=pqrs\= \kill
\>P1. \>Initialise rules to null consequent, zero degree. \\
\> \>If prior information exists, it can be \\
\> \> programmed into the rule-base at this point. \\
\> \>P1.1 \>$\mathbf{for}\ k\ =\ 1\ \mathbf{to}\ K\ \mathbf{do}$ \\
\> \> \> \>$c_k\ =\ \mathbf{null}$; \\
\> \> \> \>$d_k\ =\ 0.0$; \\
\> \> \>$\mathbf{enddo};$\\
\>P2. \>Training. \\
\> \>$\mathbf{for}\ n\ =\ 1\ \mathbf{to}\ N\ \mathbf{do}$ \\
\> \>P2.1\>$\mathbf{for}\ i\ =\ 1\ \mathbf{to}\ p\ \mathbf{do}$ \\
\> \> \> \>$m_i\
=\max_{j=1}^{M_i}\{m_{X_j}(x_{in})\}$ \\
\> \> \> \>$j_i\ =\ index\ of\ fuzzy\ set\ which\
                                                          achieves\
maximum.$\\
\> \> \>$\mathbf{enddo};$\\
\> \>P2.2 \>$m_y = max_{j=1}^{M_y}\{m_{Y_j}(y_n)$\\
\> \> \>$j_y =$ index of fuzzy set which achieves maximum.\\
\> \>P2.3 \>$k =$ cell corresponding to $j_1$, $j_2$, \ldots $j_p$ \\
\> \> \>$d'_k = m_y \prod m_i$ \\
\> \>P2.4 \>$\mathbf{if}\ d'_k\ >\ d_k\ \mathbf{then}\ d_k\ =\ d'_h;\
c_k\ =\ j_y;
                                                                 
\mathbf{endif}$\\
\> \>$\mathbf{enddo};$\\
\end{tabbing}

\caption{Wang-Mendel Training Algorithm} \label{fig:wang-mendel}
\end{figure}

Hope this helps,

Jon C.

-- 
Jonathan G. Campbell, School of Computer Science, The Queen's University
of Belfast, BT7 1NN  Tel +44 (0)28 90 274623  jg.campbell@qub.ac.uk
http://www.cs.qub.ac.uk/~J.Campbell
Physical office: Room G26, Bernard Crossland Building, 18 Malone Road.

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