Drawing membership functions and fuzzy sets with LaTeX

Question

1. How can I visualize in LaTeX Fuzzy Logic diagrams such as the following picture?
2. Also how I can visualize sets?

Is the better way to show Fuzzy diagrams as an image?

Answer 1

One possibility using PGF/TikZ:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw[->] (0,0) -- node[below] {quantized} (4.5,0) 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[fill=yellow] (0,1) -- (4,1) -- (4,0) -- (0,0) -- cycle;
\foreach \x in {0.5,1,1.5,2,2.2,3.4}
  \draw (\x,0) -- (\x,1);
\begin{scope}[xshift=5.5cm]
\draw[->] (0,0) -- node[below] {granulated} (4.5,0) 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[fill=yellow!40] (0,1) -- (1,1) -- (1.75,0) -- (0,0) -- cycle;
\draw[fill=yellow!40] (2.25,0) -- (3,1) -- (4,1) -- (4,0) -- cycle;
\draw[fill=yellow!40] (1.25,0) -- (1.8,1) -- (2.3,1) -- (3,0) -- cycle;
\draw (1,1) -- (1.75,0) -- (2.25,0) -- (3,1);
\node[above,font=\footnotesize] at (0.5,1) {young};
\node[above,font=\footnotesize] at (2,1) {middle-aged};
\node[above,font=\footnotesize] at (3.5,1) {old};
\end{scope}
\node[anchor=south] at (current bounding box.north)
  {\textbullet\ continuous $\rightarrow$ quantized $\rightarrow$ granulated};
\end{tikzpicture}

\end{document}

For your second question (the one about sets), can you please add to your question an image of the kind of image you are trying to produce?