Help with alpha-cuts in fuzzy sets

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basically all I need to know is what are the standard methods to achieve the below.

So, I have a fuzzy set A containing (say) four elements. For each element I have a degree of membership. The degrees of membership sum to one. I want to get a crisp version of A. I'm aware we have alpha-cuts. But is there any standard method to find alpha?

(in a nutshell: the elements are actually features in a data set, and the degrees of membership is how relevant each feature is. I'm trying to do feature selection here.)

Thanks!

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1 Answer

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Given a fuzzy set $A$ on an universal set $X$, their $\alpha$-cuts are defined as follows: $A_\alpha=\{x\in X\ | \ A(x)\geq\alpha\}$

Therefore, taking $\alpha$ as the degrees of the elements, you have different crisp subsets of $X$.

In particular, for $\alpha=0$ you have $A_\alpha=X$.

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