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\begin{document}
Exercises from conversions from vertical to horizontal representation of fuzzy sets.

\begin{exercise}
Convert from vertical to horizontal representation, $A\in\mathcal{F}(\mathbb{R})$:
$$\mu_A(x)=
\begin{cases}
1/3 & \text{if } x=8 \text{ or } x=12,\\
2/3 & \text{if } x=9 \text{ or } x=11 ,\\
1 & \text{if } x=10 ,\\
0 & \text{otherwise.}
\end{cases}
$$
\end{exercise}

\begin{exercise}
Convert from vertical to horizontal representation, $D\in\mathcal{F}(\mathbb{R})$:
$$\mu_D(x)=
\begin{cases}
0 & \text{if } x\le0 \text{ or } x\ge5,\\
x/2 & \text{if } 0<x\le2 ,\\
1 & \text{if } 2<x\le3 ,\\
(5-x)/2 & \text{if } 3<x<5 .
\end{cases}
$$
\end{exercise}

\end{document}