add new repoHEAD master

author: Sven Eisenhauer <sven@sven-eisenhauer.net> 2023-11-10 15:11:48 +0100
committer: Sven Eisenhauer <sven@sven-eisenhauer.net> 2023-11-10 15:11:48 +0100
commit: 33613a85afc4b1481367fbe92a17ee59c240250b (patch)
tree: 670b842326116b376b505ec2263878912fca97e2 /Master/Computational Intelligence/NeuroFuzzy/presentation
download: Studium-master.tar.gz
Studium-master.tar.bz2
35 files changed, 3415 insertions, 0 deletions
diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/10_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/10_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/11_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/11_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/13_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/13_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/14_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/14_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/2_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/2_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/3_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/3_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/4_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/4_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/6_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/6_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/7_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/7_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/8_anfisANFIS_Noll.pdf b/Master/Computational Intelligence/NeuroFuzzy/presentation/8_anfisANFIS_Noll.pdf
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diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/literature.bib b/Master/Computational Intelligence/NeuroFuzzy/presentation/literature.bib
new file mode 100644
index 0000000..e38dab5
--- /dev/null
+++ b/Master/Computational Intelligence/NeuroFuzzy/presentation/literature.bib
@@ -0,0 +1,49 @@
+@Book{Bor03,
+ALTauthor = {Christian Borgelt and Frank Klawonn and Rudolf Kruse and Detlef Nauck},
+title = {Neuro-Fuzzy-Systeme},
+publisher = {Vieweg Verlag},
+year = {2003},
+OPTaddress = {Wiesbaden}
+}
+@Article{Kar10,
+author = {Dr. T. Karthikeyan},
+title = {Efficient Bio Metric IRIS Recognition System Using Fuzzy Neural Network},
+journal = {Int. J. of Advanced Networking and Applications},
+year = {2010},
+OPTkey = {•},
+OPTvolume = {01},
+OPTnumber = {•},
+OPTpages = {371-376},
+OPTmonth = {•},
+OPTnote = {•},
+OPTannote = {•}
+}
+@Book{Lip06,
+ALTauthor = {Wolfram-Manfred Lippe},
+ALTeditor = {•},
+title = {Soft-Computing},
+publisher = {examen press},
+year = {2006},
+OPTkey = {•},
+OPTvolume = {•},
+OPTnumber = {•},
+OPTseries = {•},
+OPTaddress = {•},
+OPTedition = {•},
+OPTmonth = {•},
+OPTnote = {•},
+OPTannote = {•}
+}
+@Article{Nue99,
+author = {A. Nürnberger, D. Nauck, R. Kruse},
+title = {Neuro-fuzzy control based on the NEFCON-model: recent developments},
+journal = {Soft-Computing},
+year = {1999},
+OPTkey = {•},
+OPTvolume = {2},
+OPTnumber = {•},
+OPTpages = {168-182},
+OPTmonth = {•},
+OPTnote = {•},
+OPTannote = {•}
+}
diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/neuro-fuzzy-presentation.tex b/Master/Computational Intelligence/NeuroFuzzy/presentation/neuro-fuzzy-presentation.tex
new file mode 100644
index 0000000..25eb3f2
--- /dev/null
+++ b/Master/Computational Intelligence/NeuroFuzzy/presentation/neuro-fuzzy-presentation.tex
@@ -0,0 +1,64 @@
+\documentclass[11pt,a4paper]{beamer}
+\usepackage[utf8x]{inputenc}
+\usepackage{ucs}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage[ngerman]{babel}
+\usepackage[final]{pdfpages}
+\graphicspath{{img//}}
+\bibliographystyle{alphadin}
+
+%theme%
+\usetheme{Warsaw}
+
+\title{Neuro-Fuzzy Systeme}
+\author[S. Sonski \and W. Noll \and S. Eisenhauer]{Stefan Sonski \and Walter Noll \and Sven Eisenhauer}
+\date[07.06.11]{07. Juni 2011}
+\logo{\pgfimage[width=24mm]{img//logo_hda_fbi}}
+\begin{document}
+	%title%
+	\frame{
+		\titlepage
+	}
+	
+	%content%
+	\frame{
+		\frametitle{Agenda}
+		\tableofcontents
+	}
+	
+	%begin of user content%
+	
+	\input{part1}
+	\input{part2}
+	\input{part3}
+	
+	\frame{
+		\frametitle{Anwendungen}
+		\begin{columns}
+		\column{.5\textwidth}
+			\includegraphics[width=\linewidth]{ricecooker1}
+		\column{.5\textwidth}
+			\begin{itemize}
+				\item Regelung und Steuerung
+				\item DAX-Vorhersage
+				\item Iris-Erkennung
+				\item \dots
+			\end{itemize}
+		\end{columns}
+	}	
+	
+	\frame{
+		\begin{Huge}
+			\begin{center}
+				Vielen Dank!
+			\end{center}
+		\end{Huge}
+	}
+	\frame{
+		\frametitle{Quellen}
+		\nocite{*}
+		\bibliography{literature}
+	}
+\end{document}
+\ No newline at end of file
diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/part1.tex b/Master/Computational Intelligence/NeuroFuzzy/presentation/part1.tex
new file mode 100644
index 0000000..156d571
--- /dev/null
+++ b/Master/Computational Intelligence/NeuroFuzzy/presentation/part1.tex
@@ -0,0 +1,211 @@
+\section{Motivation}
+	\begin{frame}{Grenzen bisheriger Konzepte}
+		\begin{block}{Fuzzy-Regler}
+			\begin{itemize}
+				\item Nicht lernfähig
+				\item Fuzzy-Mengen und -Regeln müssen bekannt sein
+				\item Vollständigkeit
+			\end{itemize}
+		\end{block}
+		\begin{block}{Neuronale Netze}
+			\begin{itemize}
+				\item A-priori Wissen nicht nutzbar
+				\item Lernerfolg ungewiss
+				\item \textit{Blackbox}
+			\end{itemize}
+		\end{block}
+	\end{frame}
+
+\section{Grundlagen}
+
+	\subsection{Kooperative Ansätze}
+	
+		\begin{frame}{Kooperative Ansätze}
+			\begin{block}{Eigenschaften}
+				\begin{itemize}
+					\item Neuronales Netz und Fuzzy-Regler bleiben als eigenständige Systeme erhalten
+					\item Geringer Kopplungsgrad
+					\item Vor- und Nachteile bleiben weitgehend erhalten
+				\end{itemize}
+			\end{block}
+			\begin{block}{Einfachste Kopplung}
+				Neuronales Netz zur Aufbereitung von Ein- oder Ausgaben eines Fuzzy-Reglers
+			\end{block}
+		\end{frame}
+		
+		\begin{frame}{Kooperative Ansätze, offline}
+			\begin{columns}
+				\column{.5\textwidth}
+					\begin{block}{Fuzzy-Mengen aus Beispieldaten offline lernen}
+					\includegraphics[width=\linewidth]{koop-fuzzysets.png}
+					\begin{itemize}
+						\item Bestimmung geeigneter Parameter der Zugehörigkeitsfunktionen
+						\item Approximation der Zugehörigkeitsfunktionen
+					\end{itemize}
+					\end{block}									
+				\column{.5\textwidth}
+					\begin{block}{Fuzzy-Regeln aus Beispieldaten offline lernen}
+					\includegraphics[width=\linewidth]{koop-fuzzyrules.png}
+					\\Clustering-Verfahren (selbstorganisierende Karten) zur Bestimmung der Fuzzy-Regeln
+					\end{block}	
+			\end{columns}
+		\end{frame}		
+
+		\begin{frame}{Kooperative Ansätze, online}
+			\begin{columns}
+				\column{.5\textwidth}
+					\begin{block}{Fuzzy-Mengen online lernen}
+					\includegraphics[width=\linewidth]{koop-fuzzysets-online.png}
+					\end{block}				
+				\column{.5\textwidth}
+
+					\begin{block}{Fuzzy-Regeln online lernen}
+					\includegraphics[width=\linewidth]{koop-fuzzyrules-online.png}
+					\end{block}
+			\end{columns}
+		\end{frame}	
+
+	\subsection{Hybride Ansätze}
+		\begin{frame}{Hybrider Neuronaler Fuzzy-Regler}
+			\begin{block}{Schema}
+				\includegraphics[height=0.75\textheight]{hybrid-neuro-fuzzy-ctrl.png}
+			\end{block}
+		\end{frame}
+		
+\section{Generisches Fuzzy-Perzeptron}
+	\subsection{XOR-Problem}
+		\begin{frame}{Generisches Fuzzy Perzeptron}
+			\begin{columns}
+				\column{.2\textwidth}
+					\includegraphics[width=\linewidth]{xor.png}
+				\column{.8\textwidth}
+					\begin{tabular}{|p{.3cm}|p{.3cm}|p{.8cm}|p{.8cm}|p{1.2cm}|p{1.2cm}|p{1.25cm}|}
+						\hline $x_1$ & $x_2$ & $out_{u_{11}}$ & $out_{u_{12}}$ & $out_{u_{21}}$ & $out_{u_{22}}$ & $out_{u_{31}}$ = y \\ 
+						\hline 0 & 0 & 0 & 0 & min(0,1)\linebreak = 0 & min(0,1)\linebreak = 0 & max(0,0)\linebreak = 0 \\ 
+						\hline 0 & 1 & 0 & 1 & min(0,0)\linebreak = 0 & min(1,1)\linebreak = 1 & max(0,1)\linebreak = 1\\ 
+						\hline 1 & 0 & 1 & 0 & min(1,1)\linebreak = 1 & min(0,0)\linebreak = 0 & max(1,0)\linebreak = 1 \\ 
+						\hline 1 & 1 & 1 & 1 & min(1,0)\linebreak = 0 & min(1,0)\linebreak = 0 & max(0,0)\linebreak = 0 \\ 
+						\hline 
+					\end{tabular}
+			\end{columns}
+		\end{frame}
+		
+	\subsection{Beschreibung}
+		\begin{frame}{Fuzzy-Neuronen}
+			\begin{itemize}
+				\item Eingabeschicht $U_1 = \left\lbrace x_1,\dots,x_n \right\rbrace$
+				\item Versteckte Schicht $U_2 = \left\lbrace R_1,\dots,R_r \right\rbrace$
+				\item Ausgabeschicht $U_3 = \left\lbrace y_1,\dots,y_m \right\rbrace$
+				\item Verarbeitung je Neuron $u$: $net_u \to act_u \to out_u$
+			\end{itemize}
+		\end{frame}
+		
+		\begin{frame}{Gewichte}
+			\begin{itemize}
+				\item Definiert durch Fuzzy-Mengen $\mu$ für Eingabeschicht $\to$ Versteckte Schicht
+				\item Definiert durch Fuzzy-Mengen $\nu$ für Versteckte Schicht $\to$ Ausgabeschicht
+			\end{itemize}
+			\begin{displaymath}
+			w_{vu} = 
+			\begin{cases}
+			\mu^{\left(i\right)}_{j} \qquad \qquad \qquad \textrm{für}~ u=x_i,v=R_j
+			\\
+			\nu^{\left(k\right)}_{j} \qquad \qquad \qquad \textrm{für}~ u=R_j,v=y_k
+			\\
+			\textrm{undefiniert} \qquad \quad \textrm{sonst}
+			\end{cases}
+			\end{displaymath}
+			$1 \leq i \leq n$, $1 \leq j \leq r$, $1 \leq k \leq m$
+			\\
+			$\mu^{\left(i\right)}_{j} \in F\left(\mathbb{R}\right)$,
+			$\nu^{\left(k\right)}_{j} \in F\left(\mathbb{R}\right)$
+			\\mit $F\left(\mathbb{R}\right) := \textrm{die Menge aller Fuzzy-Mengen über } \mathbb{R}$
+		\end{frame}
+		
+		\frame{
+			\frametitle{Eingabeschicht $u \in U_1$}
+			\begin{block}{Netzeingabefunktion}
+				Abbildung von $\mathbb R$ auf $\mathbb R$ für externe Eingabe $ext_u$ \\
+				$f^{\left(u\right)}_{net}: net_u = ext_u$
+			\end{block}
+			\begin{block}{Aktivierungsfunktion}
+				Abbildung von $\mathbb R$ auf $\mathbb R$ für Netzeingabe $net_u$ \\
+				$f^{\left(u\right)}_{act}: act_u = net_u$
+			\end{block}
+			\begin{block}{Ausgabefunktion}
+				Abbildung von $\mathbb R$ auf $\mathbb R$ für Aktivierung $act_u$ \\
+				$f^{\left(u\right)}_{out}: out_u = act_u$
+			\end{block}
+		}
+		\frame{
+			\frametitle{Versteckte Schicht $u \in U_2$}
+			\begin{block}{Netzeingabefunktion}
+				Abbildung von $\left(\mathbb R \times F\left(\mathbb{R}\right)\right)$ auf $\left[0,1\right] \in \mathbb{R}$ 
+				\\Gewicht zwischen $u$ und $u^{'} \in U_1$
+				\\t-Norm
+			\end{block}
+			\begin{block}{Aktivierungsfunktion}
+				Abbildung von $\mathbb R$ auf $\mathbb R$ für Netzeingabe $net_u$ \\
+				$f^{\left(u\right)}_{act}: act_u = net_u$
+			\end{block}
+			\begin{block}{Ausgabefunktion}
+				Abbildung von $\mathbb R$ auf $\mathbb R$ für Aktivierung $act_u$ \\
+				$f^{\left(u\right)}_{out}: out_u = act_u$
+			\end{block}
+		}
+		\frame{
+			\frametitle{Ausgabeschicht $u \in U_3$}
+			\begin{block}{Netzeingabefunktion}
+				t-Conorm über die Ausgaben aller $u^{'} \in U_2$ mit dem Gewicht $w_{uu^{'}}$\\
+				
+			\end{block}
+			\begin{block}{Aktivierungsfunktion}
+				$f^{\left(u\right)}_{act}: act_u = net_u$
+			\end{block}
+			\begin{block}{Ausgabefunktion}
+				Abbildung von $F\left(\mathbb{R}\right)$ auf $\mathbb R$ für Aktivierung $act_u$ \\
+				Geeignete Defuzzifizierung der Aktivierung $act_u$
+			\end{block}
+		}
+		
+	\subsection{Lernverfahren}
+		\begin{frame}{Fuzzy-Fehler}
+			\begin{displaymath}
+			E^{\left(p\right)}_{u}=1-\exp{\left(\beta\left(\frac{t^{\left(p\right)}_{u}-o^{\left(p\right)}_{u}}{range_{u}}\right)^{2}\right)}
+			\end{displaymath}
+			mit
+			\begin{itemize}
+				\item $u \in U_3$
+				\item $t$ Zielwert
+				\item $o$ Ausgabewert
+				\item $range_u$ Differenz zwischen maximalem und minimalem Ausgabewert des Neuron $u$
+				\item $\beta$ Toleranzfaktor
+			\end{itemize}
+		\end{frame}
+		
+		\begin{frame}{Fuzzy-Backpropagation}
+			\begin{enumerate}
+				\item Wähle ein beliebiges Muster $p$ einer gegebenen festen Lernaufgabe und propagiere den Eingabevektor $i^{p}$
+				\item Bestimme
+				\begin{displaymath}
+					\delta^{\left(p\right)}_{u} = 
+					\begin{cases}
+					sgn\left( t^{p}_{u} - out^{p}_{u} \right) * E^{\left(p\right)}_{u}
+					\qquad \textrm{für}~ u \in U_3
+					\\
+					\sum_{v \in U_{3} } act^{\left(p\right)}_{u}*\delta^{\left(p\right)}_{v}
+					\qquad \quad ~\textrm{für}~ u \in U_2
+					\end{cases}
+				\end{displaymath}
+				\item Bestimme
+				\begin{displaymath}
+				\Delta_{p}w_{vu} = f\left( \delta^{\left(p\right)}_{u}, act^{\left(p\right)}_u, net^{\left(p\right)}_u \right)
+				\end{displaymath}
+				
+			\end{enumerate}
+			Wiederhole diese Schritte bis der Gesamtfehler 
+			\begin{displaymath}
+			E=\sum_{p}\sum_{u \in U_{3}}E^{\left(p\right)}_{u}
+			\end{displaymath}
+			hinreichend klein ist oder ein anderes Abbruchkriterium erfüllt wird.
+		\end{frame}
+\ No newline at end of file
diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/part2.tex b/Master/Computational Intelligence/NeuroFuzzy/presentation/part2.tex
new file mode 100644
index 0000000..0db1605
--- /dev/null
+++ b/Master/Computational Intelligence/NeuroFuzzy/presentation/part2.tex
@@ -0,0 +1,170 @@
+\section{Das NEFCON-Modell}
+\begin{frame}{NEFCON-Eigenschaften}
+	\begin{columns}
+		\column{.5\textwidth}
+		\begin{itemize}
+			\item Basiert auf dem 3-Schichten-Fuzzy-Perzeptron
+			\item Verwendet den Ansatz des reinforcement learnings
+			\item Besteht auf zwei Phasen
+		\end{itemize}
+		\column{.5\textwidth}
+		\includegraphics[height=0.75\textheight]{xor.png}
+	\end{columns}
+\end{frame}
+\begin{frame}{Die Phasen}
+	\begin{block}{Die erste Phase}
+		\begin{itemize}
+			\item Es bestehen zwei Möglichkeiten
+			\begin{itemize}
+				\item Manuell erstellte Regelbasis wird vervollständigt
+				\item Leere Regelbasis wird aufgebaut	
+			\end{itemize}	
+		\end{itemize}
+	\end{block}
+	\begin{block}{Die zweite Phase}
+		\begin{itemize}
+			\item Regeloptimierung indem Fuzzy-Mengen
+			\begin{itemize}
+				\item Verschoben werden
+				\item Modifiziert werden	
+			\end{itemize}
+		\end{itemize}
+	\end{block}
+\end{frame}
+	\subsection{Erlernen der Regelbasis}
+	\begin{frame}{Erlernen der Regelbasis}
+		\begin{block}{Methoden die Regelbasis zu lernen}
+			\begin{itemize}
+				\item Durch leere Regelbasis
+				\item Durch volle Regelbasis\footnote{Bisher nicht implementiert}
+				\item Durch zufällige Regelbasis\footnote{Jede mögliche Regel enthalten}
+			\end{itemize}
+		\end{block}	
+	\end{frame}
+	\begin{frame}{Dekrementierendes Regellernen}
+		\begin{itemize}
+			\item Lernen durch volle Regelbasis
+			\item Phase 1:
+			\begin{itemize}
+				\item Läuft feste Periode oder Anzahl Iterationen
+				\item Regeln werden entfernt, wenn nicht zur optimalen Ausgabe passend
+			\end{itemize}
+			\item Phase 2:
+			\begin{itemize}
+				\item Regeln mit gleicher Prämisse werden zusammegefasst
+				\item Zufällige Auswahl einer Regel aus der Regelgruppe mit gleicher Prämisse
+				\item Berechnung des Fehlers jeder Regel
+				\begin{itemize}
+					\item Anhand der Gewichtung für die aktuelle Ausgabe
+					\item Regel mit nicht kleinster Fehleranzahl der Regelgruppe werden entfernt
+					\item Selten verwendete Regeln werden zusätzlich entfernt
+				\end{itemize}
+			\end{itemize}
+		\end{itemize}
+	\end{frame}
+	\begin{frame}{Inkrementierendes Regellernen}
+		\begin{itemize}
+			\item Lernen durch leere Regelbasis
+			\item Geeignete Fuzzy-Mengen für Ein- und Ausgabe benötigt\footnote{Mindestens Anzahl muss stimmen}
+			\item Alle möglichen Kombinationen werden als Regelbasis definiert
+			\begin{itemize}
+				\item Phase 1:
+				\begin{itemize}
+					\item Entfernen der Regeln mit falschen Vorzeichen
+				\end{itemize}
+				\item Phase 2 entspricht der zweiten Phase des dekrementierenden Regellernens
+			\end{itemize}
+		\end{itemize}
+	\end{frame}
+	\subsection{Erlernen von Fuzzy-Mengen}
+	\begin{frame}{Erlernen von Fuzzy-Mengen}
+		\begin{itemize}
+			\item Vorraussetzung ist eine korrekte Regelbasis
+			\item "`Gute"' Regeln werden belohnt, "`schlechte"' bestraft
+			\item Güte der Regel wird durch einen Fuzzy-Backpropagationalgorithmus bestimmt
+		\end{itemize}
+	\end{frame}
+	\begin{frame}{Erlernen von Fuzzy-Mengen}
+		\begin{itemize}
+			\item Bewertung des Beitrags $t_k$ der Regel $R_k$ zum Ergenbis\\
+				$t_k = u^{-1}_{k}(o_k)$
+			\item Weitere Informationen zum Ergebnis sind zur Berwertung notwendig
+			\item Stellgröße mit Wert 0 = optimaler Zustand
+			\item richtiges Vorzeichen = "`gut"'
+			\item Einfluß "`guter"' Regeln wird vergrößert
+			\item Einfluß "`schlechter"' Regeln verkleinert
+		\end{itemize}
+	\end{frame}
+	\begin{frame}{Lernverfahren}
+		\begin{block}{Schritt 1}
+			\begin{itemize}
+				\item Berechne $o$ für aktuelle Messwerte.
+				\item $o$ auf System anwenden und Messwerte berechnen
+			\end{itemize}
+		\end{block}
+		\begin{block}{Schritt 2}		
+			\begin{itemize}
+				\item Berechne Fuzzy-Fehler
+			\end{itemize}
+		\end{block}
+		\begin{block}{Schritt 3}
+			\begin{itemize}
+				\item Bestimme das Vorrücken des Stellwertes im neuen Systemzustand.
+			\end{itemize}
+		\end{block}
+	\end{frame}
+	\begin{frame}{Lernverfahren}
+		\begin{block}{Schritt 4}
+			\begin{itemize}
+				\item Berechne für Regel $R_k$ Beitrag $t_k$ mit Fehlersignal $F_k$
+				\begin{displaymath}
+					F_k :=
+					\begin{cases}
+					-o * E \qquad \text{Vorzeichen von $t_k$ richtig}
+					\\
+					o * E \qquad \quad \text{Vorzeichen von $t_k$ falsch}
+					\end{cases}
+				\end{displaymath}
+			\end{itemize}
+		\end{block}
+		\begin{block}{Schritt 5}
+			\begin{itemize}
+				\item Modifizierung aller  Eingabe-Fuzzy-Mengen\\
+					$\tilde{A}_{i*}^{(k)} = (l_{i*}^{(k)},m_{i*}^{(k)},r_{i*}^{(k)})$
+				\item durch
+				\begin{displaymath}
+					\Delta l_{i*}^{(k)} = -\eta * F_k * (m_{i*}^{(k)} - l_{i*}^{(k)})
+				\end{displaymath}
+				\begin{displaymath}
+					\Delta r_{i*}^{(k)} = -\eta * F_k * (r_{i*}^{(k)} - m_{i*}^{(k)})
+				\end{displaymath}
+			\end{itemize}
+		\end{block}
+	\end{frame}
+	\begin{frame}{Lernverfahren}
+		\begin{block}{Schritt 6}
+			\begin{itemize}
+				\item Modifizierung aller Ausgabe-Fuzzy-Mengen
+					$\tilde{B}_{i*}^{(k)} = (m_{i*}^{(k)},b_{i*}^{(k)})$
+				\item durch
+				\begin{displaymath}
+					\Delta b_{j*}^{(k)} 
+					\begin{cases}
+						\eta * F_k * (b_{j*}^{(k)} - m_{j*}^{(k)}) \qquad b_{j*}^{(k)} < m_{j*}^{(k)}\\
+						\eta * F_k * (m_{j*}^{(k)} - b_{j*}^{(k)}) \qquad b_{j*}^{(k)} < m_{j*}^{(k)}
+					\end{cases}
+				\end{displaymath}
+			\end{itemize}
+		\end{block}
+	\end{frame}
+\begin{frame}{Nachteile}
+\begin{itemize}
+	\item Fuzzy-Mengen müssen monoton sein
+		\begin{itemize}
+			\item keine Gauß- \& Dreiecks-Mengen möglich
+		\end{itemize}
+	\item Nur ein Ausgabewert möglich
+	\item Regeln können nicht überprüft werden
+	\item Fehlende Fuzzy-Mengen können nicht erzeugt werden
+\end{itemize}
+\end{frame}
diff --git a/Master/Computational Intelligence/NeuroFuzzy/presentation/part3.tex b/Master/Computational Intelligence/NeuroFuzzy/presentation/part3.tex
new file mode 100644
index 0000000..75d2097
--- /dev/null
+++ b/Master/Computational Intelligence/NeuroFuzzy/presentation/part3.tex
@@ -0,0 +1,43 @@
+\section{ANFIS}
+\begin{frame}
+\includegraphics[width=\textwidth]{1_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{2_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{3_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{4_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{5_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{6_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{7_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{8_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{9_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{10_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{11_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{12_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{13_anfisANFIS_Noll.pdf}
+\end{frame}
+\begin{frame}
+\includegraphics[width=\textwidth]{14_anfisANFIS_Noll.pdf}
+\end{frame}
+\ No newline at end of file
author	Sven Eisenhauer <sven@sven-eisenhauer.net>	2023-11-10 15:11:48 +0100
committer	Sven Eisenhauer <sven@sven-eisenhauer.net>	2023-11-10 15:11:48 +0100
commit	33613a85afc4b1481367fbe92a17ee59c240250b (patch)
tree	670b842326116b376b505ec2263878912fca97e2 /Master/Computational Intelligence/NeuroFuzzy/presentation
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