Re: Why alpha-cut?

Geraldo =?iso-8859-1?Q?Xex=E9o?= (xexeo@cos.ufrj.br)
Fri, 15 Jan 1999 21:47:37 +0100 (MET)

One of the best ways of understanding why we use alpha-cuts is to vary
it inside an application. It is a very useful tool and similar procedures can be
found in many other sciences.

For example, when using some fuzzy variation of SQL, alpha-cuts can
be used to represent user interest and even to allow for a faster solution when
joins are involved.

In general, alpha-cutting is filtering. Depending on the problem you
can have different interpretations of the meaning of the alpha-cut. The most
common could be "minimal level of interest" of a signal.

Of course, alpha-cut a membership function is equivalent to create a new
membership function. So, why we use this terminology? Membership
functions are supposed to represent (mean) something to human beings.
Alpha-cut represents what part of the membership function we desire
to work. Dividing both concepts provide a more general solution. Equivalent
discussion can be done about hedges.

Jerry

--
Geraldo Xexéo, D.Sc. (DCC/IM/UFRJ e PESC/COPPE/UFRJ)
mailto:xexeo@cos.ufrj.br http://www.cos.ufrj.br/~xexeo
ICQ#:12662368 Tel. 590 2552 R 236
"Se você acha a Educação cara, experimente a ignorância." C.W. Elliot

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