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\begin{document}
Exercises from conversions of representations of discrete fuzzy sets.

%\begin{enumerate}
%\item 
\begin{exercise}
Personal preferences of (all~$4$) candidates participating in elections are:
\begin{align*}
 \mu_C(A.B.) &= 0.4\,,\\
 \mu_C(C.D.) &= 0.6\,,\\
 \mu_C(E.F.) &= 0.8\,,\\
 \mu_C(G.H.) &= 0.2\,.
\end{align*}
Find the horizontal representation of this fuzzy set.
\end{exercise}

%\item 
\begin{exercise}[``satisfaction with the grades''; old scale]
Fuzzy set $A$ is given by its collection of cuts:
$$\rezR_A(\alpha)=
\begin{cases}
 \{1,2,3,4\}\,, & \alpha=0\,,\\
 \{1,2,3\}\,, & \alpha\in(0,0.3]\,,\\
 \{1,2\}\,, & \alpha\in(0.3,0.6]\,,\\
 \{1\}\,, & \alpha\in(0.6,1]\,.\\
\end{cases}
$$
Find its vertical representation.
\end{exercise}

%\item 
\begin{exercise}[``satisfaction with the grades''; new scale]
Fuzzy set $B$ is given by its collection of cuts:
$$\rezR_B(\alpha)=
\begin{cases}
 \{A,B,C,D,E,F\}\,, & \alpha=0\,,\\
 \{A,B,C,D,E\}\,, & \alpha\in(0,0.2)\,,\\
 \{A,B,C\}\,, & \alpha\in[0.2,0.4)\,,\\
 \{A,B,C,D\}\,, & \alpha\in[0.4,0.6)\,,\\
 \{A,B\}\,, & \alpha\in[0.6,0.8)\,,\\
 \{A\}\,, & \alpha\in[0.8,1]\,.\\
\end{cases}
$$
Find its vertical representation.
\end{exercise}
%\end{enumerate}

\end{document}
