[Tex/LaTex] Sigmoid membership functions with tikz

tikz-pgf

I would like to draw fuzzy membership functions using tikz. The problem has already been solved in Trapezoidal solution for trapezoidal MF, but I need something similar for sigmoidally shaped functions. I don't have a clue how to do that …

enter image description here

I have this code:

 \documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}

\begin{scope}[xshift=5.5cm]
\draw[->] (0,0) -- node[below] {} (5,0) node[below] {Age};
\draw[->] (0,0) -- (0,1.5) node[left] {$\mu$};
\node at (-0.2,0) {0};
\node at (-0.2,1) {1};
\draw (0,1) -- (5,1);
\draw[scale=1,domain=0:5,smooth,variable=\x,blue] plot ({\x},{1/(1+exp(-1*(\x-3)))});
\draw[scale=1,domain=0:5,smooth,variable=\x,red] plot ({\x},{1/(1+exp(-3*(\x-1.5)))});

\end{scope}

\end{tikzpicture}

\end{document}

enter image description here

but I don't undestand why the red line in the final part "fall" at a value different from 1, since it doesn't make any sense given the mathematical function used in "plot"

Best Answer

You can define your membership functions yourself and have control over how you implement it. I've defined the triangle, trapezoid, gaussian and generalized Bell, sigmoid and you can add more such as one sided functions etc. Please notice the percent signs at the end of each line for the function. If you omit them your plot will shift to the right with whitespaces everytime you execute the function becuase they will be picked up by the font.

And I would strongly recommend pgfplotsfor this. It is pretty much the choice for such uses.

Here is one example

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\pgfmathdeclarefunction{fuzzytrapezoid}{4}{%
\begingroup%
\pgfmathparse{max(min((x-#1)/(#2-#1),1,(#4-x)/(#4-#3)),0)}%
\pgfmathfloattofixed{\pgfmathresult}%
\pgfmathreturn\pgfmathresult pt\relax%
\endgroup%
}
\pgfmathdeclarefunction{fuzzytriangle}{3}{%
\begingroup%
\pgfmathparse{max(min((x-#1)/(#2-#1),(#3-x)/(#3-#2)),0)}%
\pgfmathfloattofixed{\pgfmathresult}%
\pgfmathreturn\pgfmathresult pt\relax%
\endgroup%
}
\pgfmathdeclarefunction{fuzzygaussian}{2}{%
\begingroup%
\pgfmathparse{exp(-0.5*((x-#1)/#2)^2)}%
\pgfmathfloattofixed{\pgfmathresult}%
\pgfmathreturn\pgfmathresult pt\relax%
\endgroup%
}
\pgfmathdeclarefunction{fuzzygenbell}{3}{%
\begingroup%
\pgfmathparse{1/(1+abs((x-#3)/#1)^(2*#2))}%
\pgfmathfloattofixed{\pgfmathresult}%
\pgfmathreturn\pgfmathresult pt\relax%
\endgroup%
}
\pgfmathdeclarefunction{fuzzysigmoid}{2}{%
\begingroup%
\pgfmathparse{1/(1+exp(-#1*(x-#2))}%
\pgfmathfloattofixed{\pgfmathresult}%
\pgfmathreturn\pgfmathresult pt\relax%
\endgroup%
}

\begin{document}
\begin{tikzpicture}
\begin{axis}[ymajorgrids,
ytick={0,1},tick style={draw=none},xtick=\empty,domain=0:10,no marks
]
%\addplot+[no marks] {1/(1+exp(-3*(x-1.5))};
\addplot+[] {fuzzytrapezoid(1,1.5,3,4)};
\addplot+[] {fuzzytriangle(2,5,7)};
\addplot+[samples=201] {fuzzygaussian(6.5,0.7)};
\addplot+[] {fuzzygenbell(4,-2,0.6)};
\addplot+[very thick] {fuzzysigmoid(1.5,4)};
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Numerical conditional within tikz keys

I am definitely unfamiliar with both beamer and tikz (do not quite get what the \only are supposed to do) but perhaps this could go in the direction you want:

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{chains}
\newcounter{count}

% helper macro:
\long\def\GobToSemiColon #1;{}

\newcommand\myPicture{
\begin{tikzpicture}
  \begin{scope}[start chain = going below]
  \ifnum\value{count}<1 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>3 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is between
    1 and 3};

  \ifnum\value{count}>-1 \expandafter\GobToSemiColon\fi
  \node[draw, rectangle, on chain] {display only when counter is
    negative}; 

  \ifnum\value{count}<100 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>200 \expandafter\GobToSemiColon\fi  
  \node[draw, rectangle, on chain] {display only if counter is between
    100 and 200};

  \ifnum\value{count}<3 \expandafter\GobToSemiColon\fi
  \ifnum\value{count}>20 \expandafter\GobToSemiColon\fi
  \node[draw, circle, on chain] {only when counter is in the range 3 to 20};
  \end{scope}
\end{tikzpicture}
}

\begin{document}
\begin{frame}
\only{\setcounter{count}{-3}\myPicture}
\only{\setcounter{count}{105}\myPicture}
\only{\setcounter{count}{39}\myPicture}
\only{\setcounter{count}{2}\myPicture}
\only{\setcounter{count}{5}\myPicture}
\end{frame}
\end{document}

beamer

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Numerical conditional within tikz keys

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

Related Question