### fix matlab, extension multivalued and membership formula

master
parent d140129b65
commit 32f120eded
Signed by: peter.babic
GPG Key ID: 4BB075BC1884BA40
3 changed files with 8 additions and 6 deletions
1. 3
fuzzy-logic/MATLAB/car_brake.fis
2. BIN
fuzzy-logic/fuzzy_logic.pdf
3. 11
fuzzy-logic/fuzzy_logic.tex

#### 3 fuzzy-logic/MATLAB/car_brake.fis Unescape Escape View File

 @ -4,7 +4,7 @@ Type='mamdani' Version=2.0 NumInputs=2 NumOutputs=1 NumRules=6 NumRules=7 AndMethod='min' OrMethod='max' ImpMethod='min' @ -45,3 +45,4 @@ MF5='greatlyIncreased':'trimf',[5 20 30] 3 -4, 1 (0.5) : 1 -3 1, 4 (0.25) : 1 0 2, 3 (0.1) : 1 2 1, 1 (1) : 1

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#### 11 fuzzy-logic/fuzzy_logic.tex Unescape Escape View File

 @ -60,7 +60,7 @@  \begin{columns}  \column{.6\textwidth}  \begin{itemize}  \item Fuzzy logic is an extension of Boolean logic  \item Fuzzy logic is an extension of multivalued logic  \item Natural language rules  \item Aristotle, later Lofti A. Zadeh in 1965 and 1973  \item Japan, later on west @ -137,11 +137,12 @@   \begin{frame}{Formal Definitions}  \begin{block}{Definition}  Let $U$ be the \textit{universe of discourse} and $x$ be the element in it. The \textit{membership function} $\mu_A$ is defined as:  $$\mu_A:X\rightarrow[0,1]$$  Let $U$ be the \textit{universe of discourse} and $x$ be the element in it. The \textit{membership function} $f^A$ assigning \textit{degree of membership} $\mu_A$:  $$f^A(x): \: \in U \rightarrow \mu_A(x) \in [0,1]$$ % $$\mu_A:U\rightarrow[0,1]$$  \end{block}  \begin{block}{Definition}  A fuzzy set $A$ is expressed as a set of ordered pairs, given that $\mu_A(x)$ is a degree, to which $x$ a member of $A$:  A fuzzy set $A$ is expressed as a set of ordered pairs (tuples), given that $\mu_A(x)$ is a degree, to which $x$ a member of $A$:  $$A=\{(x,\mu_A(x))\,|\,x \in U\}$$  \end{block} \end{frame} @ -272,7 +273,7 @@   \begin{frame}{Fuzzy Inference Engine}  \begin{figure}  \includegraphics[width=.65\textwidth]{inference.png}  \includegraphics[width=.6\textwidth]{inference.png}  \caption{Process of a fuzzy control. The most used method for defuzzification is \textit{center of gravity} (centroid).}  \end{figure} \end{frame}