diff --git a/fuzzy-logic/MATLAB/car_brake.fis b/fuzzy-logic/MATLAB/car_brake.fis index 0ac54f7..2c7b3cc 100644 --- a/fuzzy-logic/MATLAB/car_brake.fis +++ b/fuzzy-logic/MATLAB/car_brake.fis @@ -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 diff --git a/fuzzy-logic/fuzzy_logic.pdf b/fuzzy-logic/fuzzy_logic.pdf index b3138ff..fcc890a 100644 Binary files a/fuzzy-logic/fuzzy_logic.pdf and b/fuzzy-logic/fuzzy_logic.pdf differ diff --git a/fuzzy-logic/fuzzy_logic.tex b/fuzzy-logic/fuzzy_logic.tex index bfc34b5..3771237 100644 --- a/fuzzy-logic/fuzzy_logic.tex +++ b/fuzzy-logic/fuzzy_logic.tex @@ -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}