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Let $R$ and $S$ be two fuzzy relations defined as:

$\begin{matrix} & & & &y_1& &y_2\end{matrix}\\R=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6 &0.4 \\ 0.7&0.3 \end{bmatrix} \text{ and}$

$\begin{matrix} && && z_1& &z_2&z_3\end{matrix}\\S=\begin{matrix}y_1\\y_2\end{matrix}\begin{bmatrix} 0.8 &0.5&0.1 \\ 0.0&0.6&0.4 \end{bmatrix}$

Then, the resulting relation, $T$, which relates elements of universe $x$ to the elements of universe $z$ using max-min composition is given by:

- $\begin{matrix} && && z_1& &z_2&z_3\end{matrix}\\T=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.4 &0.6&0.4 \\ 0.7&0.7&0.7 \end{bmatrix} \\$
- $\begin{matrix} && && z_1& &z_2&z_3\end{matrix}\\T=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.4 &0.6&0.4 \\ 0.8&0.5&0.4 \end{bmatrix} \\$
- $\begin{matrix} && && z_1& &z_2&z_3\end{matrix}\\T=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6&0.5&0.4 \\ 0.7&0.5&0.3 \end{bmatrix} \\$
- $\begin{matrix} && && z_1& &z_2&z_3\end{matrix}\\T=\begin{matrix}x_1\\x_2\end{matrix}\begin{bmatrix} 0.6 &0.5&0.5 \\ 0.7&0.7&0.7\end{bmatrix}$