Let $A_{\alpha_0}$ denotes the $\alpha$-cut of a fuzzy set $A$ at $\alpha_0$. I…

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Let $A_{\alpha_0}$ denotes the $\alpha$-cut of a fuzzy set $A$ at $\alpha_0$. If $\alpha_1<\alpha_2$, then:

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In fuzzy sets, a higher $\alpha$-cut gives a smaller or equal set.

Since,

$\alpha_1<\alpha_2$

the cut at $\alpha_1$ will contain all elements of the cut at $\alpha_2$.

So,

$A_{\alpha_1}\supseteq A_{\alpha_2}$

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