Why alpha-cut?

Ulf Nordlund (ulf.nordlund@pal.uu.se)
Mon, 11 Jan 1999 13:32:25 +0100 (MET)

Hi all, (Although I don't know how many "all" are these days, with so few
postings..)

I have a question / suggestion:

I have used fuzzy methods in practical applications for some years now. I
have read many interesting papers on the subject, and I have taught it and
discussed it with others. Apart from some odd methods (like, for instance,
strange ways of performing defuzzification or aggregation with no
counterparts in "real life") I agree on most of the things said.

I have one problem though, and that is the alpha-cut.

Why do we use alpha-cuts? What is it good for? In analogy with how our
brains work, what cognitive or other operation does the alpha-cut
correspond to? - I don't think we go around making some sort of
"subconscious" alpha-cuts about things. (Or do we?) (I put this question
to this news group some months ago and did not ge one single good
answer...)

>From a practical point of view, what does an alpha cut do that we couldn't
do when defining the membership functions. (I do see that restricting the
sets' domains may in some cases result in better performance (although at
the price of poorer continuity. - And continuity is usually what we want,
no?) Anyway, I have never used the alpha-cut. Nor have I seen any "real"
appliactions where the alpha-cut is critical in any way...

Could it be that the alpha cut is something only used by the theorethical
fuzzy logicians, and that it in fact has no practical meaning or use? If
so, why do we (the people actually using fuzzy) at all bother with it?
(Why, for instance, is it included in books such as Earl Cox's - which
otherwise is excellent! (Earl, are you out there?))

Anyone care to comment on this?

Cheers,
ulf

-- 
   Ulf Nordlund, Inst. of Earth Sciences
   Uppsala University, Sweden
   <ulf.nordlund@pal.uu.se>

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