Implementation of alpha cuts

[scikit-fuzzy]

Implementation of alpha cuts

[JDWarner]

Hi @pbreach, I believe the functionality you are asking for is under skfuzzy.lambda_cut. This function returns an array of the same shape as the input membership function containing binary yes/no answering if each value was greater than the floating point value lambdacut.

Extracting the bounds from that result just requires grabbing the first and last 1s.

Perhaps you found that already. If you think a function to more precisely determine the exact boundaries would be valuable, e.g. with interpolation, feel free to reopen this Issue or I could guide you through a PR. That is doable, I just wasn't sure how large the audience would be.

[JDWarner]

(I just couldn't leave well enough alone, so I whipped up a function to do this myself. Look for it tomorrow)

[pbreach]

@JDWarner Thanks! I realized shortly after posting to use lambda cuts in the way you mentioned (still a bit new to the concept let alone the module), but I think it would be useful to have an alpha cut function that could do the interpolation.

Unfortunately I won't be able to work on a PR at this time, but I may need to use the module again in the coming months. If so then I look forward to contributing.

[JDWarner]

@pbreach can you explain what you mean by alpha-cuts? Is it a different process than what I've called lambda-cuts, or is the difference essentially just getting the boundaries?

I have a working local version which does calculate the exact boundaries, though the function name currently is lambda_cut_boundaries. Also found and fixed an edge case error in skfuzzy.lambda_cut - it was not working as expected for a cut value of 1.0. Both of these should be up tomorrow.

[pbreach]

Yes it is essentially the boundaries of a lambda cut for a given alpha level (or cut value) on the interval of [0,1].

For example, in the case of a sigmoidal membership function, alpha cut values in the set of (0,1) will give only one value, while alpha cut values of 0 and 1 should give two values corresponding to the bounds where the membership function is 0 and 1 respectively.

[pbreach]

After looking into this more it looks like alpha cuts and lambda cuts actually may be analogous... Alpha cut refers to the interval [a_alpha, b_alpha] for a particular alpha level or degree of membership.

I think the lambda_cut_boundaries function with a way to interpolate is exactly what I was referring to originally.

[JDWarner]

Closed by #50 (see discussion and implementation in that PR)