Re: Why alpha-cut?

Francesco Carriero (carriero@ssi.it)
Sat, 30 Jan 1999 19:41:27 +0100 (MET)

Geraldo Xexéo wrote:

> Of course, alpha-cut a membership function is equivalent to create a new
> membership function. So, why we use this terminology?

Yes, why?
Maybe it depends on my theoretical background, or maybe I learned it the wrong way,
but I would prefer calling it Minimum Degree of Firing of a rule; this thread so far
(but I only have available the last three messages) has dealt with this concept,
after all...
Even though an alpha-cut membership function will act as MDF mechanism, still I
would keep separate concepts related to fuzzy sets from concepts related to fuzzy
rules or, better, to a particular fuzzy inference mechanism
IMHO, the usefulness of alpha-cuts shows up mainly in the field of fuzzy sets
theory, and stems from the theorem that states the equivalence between any fuzzy set
and the OR of all its distinct alpha cuts. For instance, this equivalence allows to
handle problems like fuzzy numbers and fuzzy arithmetic resorting to well known
tools of standard maths (i.e., the interval arithmetic)

francesco

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