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setfuzzy-logic
Sachin Yadav
Sachin Yadav

Reputation: 806

Alpha cut in fuzzy logic

Can someone please explain in simple terms with an example what is aplha cut in fuzzy logic

I tried to understand on my own, by referring to this and I could only get the definition without any simple explanation with example

The definition says something like

Let µ ∈ F(X) and α ∈ [0, 1].

Then the sets [µ]α = {x ∈ X | µ(x) ≥ α} , [µ]α = {x ∈ X | µ(x) > α} are called the α-cut and strict α-cut of µ

Consider for example this fuzzy set

A = { 0/1 + 0.1/2 + 0.4/3 + 0.5/4 + 0.5/5 }

Can someone please try to explain with the above mentioned set

Thank you

Upvotes: 1

Views: 9751

Answers (1)

Matt Cremeens
Matt Cremeens

Reputation: 5151

It is the set of all xs where mu(x) is larger than alpha. In your example, assume alpha is 0.2. Then the alpha-cut is {3,4,5} because all of those xs have membership values greater than 0.2.

Upvotes: 2

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