Re: Why alpha-cut?

Mark A. Scarton (mascarton@xmission.com)
Fri, 15 Jan 1999 20:45:24 +0100 (MET)

ulf.nordlund@pal.uu.se (Ulf Nordlund) wrote:
> 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? -

To me, an alpha cut is the degree of sensitivity to the system to the behavior
under observation. At some point, as the information value diminishes, I no
longer want to be "bothered" by the data. In many systems, due to the inherent
limitations of the mechanics of observation, the information becomes suspect
below a certain level of reliability (or I just plain don't care about it).

> - 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...)

I would argue that you do, constantly. For one thing, your brain automatically
filters things before you even conciously pay any attention to them. Your
neurophysiology dictates what you observe. Beyond that, you are constantly
deciding what things to pay attention to and which to ignore. Or do you
actually read the entire content of every posting to this group? :-)

> 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...

Membership functions define the degree of participation of an observable element
in the set, not the desirability or value of the information. Let's take an
example. I have a system that visually inspects items under manufacture. I
have a vast number of aspects of the element that I sample. Using the alpha cut
associated with each to determine the value of the sampled data points, I only
pay attention to (algorithmically) those that are pertinent. Below that alpha
cut, I ignore the information. (In fact, I ignore that information _unless_ the
data above the alpha cut suggests that there may be a manufacturing defect.
Then I lower the alpha cut to increase the information bandwidth, but only with
respect to the current sampling being processed.)

> 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?))

Nah. I'd suggest contacting George Klir or the BISC group. They could help you
to hone in on practical applications, using the alpha cut to increase processing
bandwidth, improve precision, etc.

Unfortunately I'm a practicing engineer also. I can only afford a small amount
of time toward "academic investigation" ... I only get paid when the effort
results in an operational system for a client. And I most often can't be too
specific since the work is proprietary to a commercial client or is classified
by the government. So I can't go too far in this discussion.

Thanks!

############################################################################
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3) To reach the human who maintains the list, send mail to
fuzzy-owner@dbai.tuwien.ac.at
(4) WWW access and other information on Fuzzy Sets and Logic see
http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html