Re: confused by terminology!

On Mon, 06 Oct 2003 19:18:26 +0530, scooter <[EMAIL PROTECTED]>
wrote:

>I've read number of articles about FL and the terminology used is very
>confusing. (and contradictory)

No, see below.

>Is a FLV comprised of a number of fuzzy sets or is a fuzzy set
>comprised of a number of FLVs?
>
>In other words, Taking the former, I would define HEIGHT as a FLV,
>which is comprised of the fuzzy sets: SHORT, MEDIUM and TALL. Is this
>the correct terminology?

Yes. A fuzzy lingustic variable is a fuzzy set.

So SHORT, MEDIUM, TALL are fuzzy sets. They share the same domain set
R+ (set of real numbers representing height, say, in cm). In other
words they are fuzzy subsets of R+ or else fuzzy sets over R+. So
formally written:

SHORT : R+ -> [0, 1]
MEDIUM : R+ -> [0, 1]
TALL : R+ -> [0, 1]

Now HEIGHT is also a fuzzy set, but it has *another* domain. Its
domain set is { SHORT, MEDIUM, TALL }. So formally:

HEIGHT : { SHORT, MEDIUM, TALL } -> [0, 1]

This is the whole idea behind the liguistic variables. Instead of
working with R+, which is a large infinite set, we are dealing with a
very small finite set { SHORT, MEDIUM, TALL }. This is a way humans
reduce complexity.

See also:
http://www.dmitry-kazakov.de/ada/fuzzy.htm#linguistic%20variable

> (In some literature I've seen SHORT MEDIUM and TALL called FLVs and
>HEIGHT the fuzzy set! It's v confusing)

---
Regards,
Dmitry Kazakov
www.dmitry-kazakov.de