@ -68,7 +68,7 @@
\column { .35\textwidth }
\begin { figure} [b]
\includegraphics { lofti.jpg }
\includegraphics { lofti}
\caption { Lofti A. Zadeh}
\end { figure}
\end { columns}
@ -87,7 +87,7 @@
\end { itemize}
\begin { figure}
\includegraphics [width=.5\textwidth] { fuzzy-crisp.jpg }
\includegraphics [width=.5\textwidth] { fuzzy-crisp}
\caption { The classical set theory is a subset of the theory of fuzzy sets}
\end { figure}
\end { frame}
@ -95,7 +95,7 @@
\begin { frame} { Crisp Set}
Theory of Sets (formerly Classes) was conceptualized by George Cantor in 1870's.
\begin { figure}
\includegraphics [width=.75\textwidth] { crisp-set.jpg }
\includegraphics [width=.75\textwidth] { crisp-set}
\caption { Crisp set illustration. The element either is fully member of a set or is not a member at all.}
\end { figure}
\end { frame}
@ -104,7 +104,7 @@
When does a heap of grains stops being heap, if we are removing one grain at a time?
\begin { figure}
\includegraphics [width=.75\textwidth] { sorites-gradient.jpg }
\includegraphics [width=.75\textwidth] { sorites-gradient}
\caption { At what point exactly does blue becomes red? Sorites paradox \cite { podosky1985vagueness} .}
\end { figure}
@ -129,7 +129,7 @@
\begin { frame} { Fuzzy Set Interpretation}
How do we represent \textit { numerical} value in a fuzzy set? With the use of \textit { linguistic variables} \cite { lieb1993linguistic} , \textbf { not} probabilities.
\begin { figure}
\includegraphics [width=.75\textwidth] { fuzzy-set-degrees.jpg }
\includegraphics [width=.75\textwidth] { fuzzy-set-degrees}
\caption { Example interpretation of fuzzy sets. At the given temperature point, we can tell that the measured medium is "not hot", "slightly warm" and "almost cold". It does not mean that the chance the water is cold is 75\% .
\label { fig:fuzzy-set} }
\end { figure}
@ -158,7 +158,7 @@
\end { itemize}
\begin { figure}
\includegraphics [width=.95\textwidth] { fuzzy-set-op.jpg }
\includegraphics [width=.95\textwidth] { fuzzy-set-op}
\caption { The complement $ \mathbf { \mu _ { \bar A } } $ , the intersection $ \mathbf { \mu _ { A \cap B } } $ and the union $ \mathbf { \mu _ { A \cup B } } $ (green).}
\end { figure}
\end { frame}
@ -230,7 +230,7 @@
\begin { frame} { The Most Common T-norms}
$$ \mathsf { T _ { min } } ( a,b ) = min \{ a,b \} $$
\begin { figure}
\includegraphics [width=.95\textwidth] { min-tnorm.png }
\includegraphics [width=.95\textwidth] { min-tnorm}
\caption { \textbf { Minimum} (G{ \" o} del) T-norm is the most common one}
\end { figure}
\end { frame}
@ -238,7 +238,7 @@
\begin { frame} { The Most Common T-norms}
$$ \mathsf { T _ { prod } } ( a,b ) = a \cdot b $$
\begin { figure}
\includegraphics [width=.95\textwidth] { product-tnorm.png }
\includegraphics [width=.95\textwidth] { product-tnorm}
\caption { \textbf { product} T-norm}
\end { figure}
\end { frame}
@ -246,7 +246,7 @@
\begin { frame} { The Most Common T-norms}
$$ \mathsf { T _ { Luk } } ( a,b ) = max \{ 0 , \: a + b - 1 \} $$
\begin { figure}
\includegraphics [width=.95\textwidth] { luk-tnorm.png }
\includegraphics [width=.95\textwidth] { luk-tnorm}
\caption { \textbf { { \L } ukasiewics} T-norm}
\end { figure}
\end { frame}
@ -266,14 +266,14 @@
% lughofer2011evolving, mamdani inference
\begin { figure}
\includegraphics [width=.75\textwidth] { fuzzy-control-block.jpg }
\includegraphics [width=.75\textwidth] { fuzzy-control-block}
\caption { Block diagram of a fuzzy control}
\end { figure}
\end { frame}
\begin { frame} { Fuzzy Inference Engine}
\begin { figure}
\includegraphics [width=.6\textwidth] { inference.png }
\includegraphics [width=.6\textwidth] { inference}
\caption { Process of a fuzzy control. The most used method for defuzzification is \textit { center of gravity} (centroid).}
\end { figure}
\end { frame}
@ -323,27 +323,27 @@
\begin { frame} [allowframebreaks]{ MATLAB Fuzzy Toolbox}
\begin { figure}
\includegraphics [width=.75\textwidth] { sw-1.png }
\includegraphics [width=.75\textwidth] { sw-1}
% \caption { •}
\end { figure}
\begin { figure}
\includegraphics [width=.75\textwidth] { sw-2.png }
\includegraphics [width=.75\textwidth] { sw-2}
% \caption { •}
\end { figure}
\begin { figure}
\includegraphics [width=.75\textwidth] { sw-3.png }
\includegraphics [width=.75\textwidth] { sw-3}
% \caption { •}
\end { figure}
\begin { figure}
\includegraphics [width=.75\textwidth] { sw-4.png }
\includegraphics [width=.75\textwidth] { sw-4}
% \caption { •}
\end { figure}
\begin { figure}
\includegraphics [width=.5\textwidth] { sw-5.png }
\includegraphics [width=.5\textwidth] { sw-5}
% \caption { •}
\end { figure}
\begin { figure}
\includegraphics [width=.75\textwidth] { sw-6.png }
\includegraphics [width=.75\textwidth] { sw-6}
% \caption { •}
\end { figure}
\end { frame}