Re: confused by terminology!

scooter <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> I've read number of articles about FL and the terminology used is very
> confusing. (and contradictory)
> 
> 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?
> 
>  (In some literature I've seen SHORT MEDIUM and TALL called FLVs and
> HEIGHT the fuzzy set! It's v confusing)
> 
> thanks

I don't blame scooter for being confused. Fuzzy people are sometimes
quite loose in their definitions of terms, but sometimes so precise
that it is hard to guess what they mean.

What is a fuzzy set? It is an ordinary crisp set, whose members have
"grades of membership" ranging from zero to one indicating the degree
to which each member belongs to the set in a particular instance. A
fuzzy set is then strictly speaking a fuzzy subset of the universal
set.

This definition is very general. Actually, there are several types of
fuzzy sets, at different levels of abstraction. If there is a discrete
number of members, such as the members of discrete fuzzy set Speed,
say {SLOW, MEDIUM, FAST} or discrete fuzzy set Diagnosis, say
{MAJOR_DEPRESSION, SCHIZOPHRENIA, BIPOLAR_DISORDER}, we have a
discrete fuzzy set; if the members are all numbers from the real line
we have a continuous fuzzy set. Right away we hit a problem; many
fuzzy people assume that the term "fuzzy set" means a continous fuzzy
set.

Now we hit another confusing problem. While the definition of a
linguistic variable seems ferociously general, in fact it is very
specialized; there is an implicit assumption that the linguistic
variable and its associated members (linguistic terms) will describe
numbers. So in the examples if discrete fuzzy sets given above, Speed
could be a linguistic variable, but Diagnosis could not.

While the formal definition of a linguistic variable includes five
components, only three of these are usually important in practice.

First, there is the name of the linguistic variable itself, such as
Speed.

The members of Speed are the second element, the "term-set". The
term-set lists the possible members of the linguistic variable.
Linguistic variable Speed is a discrete fuzzy set whose members
(term-set) are SLOW, MEDIUM and FAST. Now we hit a second problem; the
members of the linguistic variable are sometimes called linguistic
terms and sometimes called linguistic values.

Finally, we have the third important element of a linguistic variable;
memership functions. These functions map an input number onto grades
of membership of the linguistic terms. Membership functions are almost
always continuous fuzzy sets. Another source of confusion; the name of
a member of a linguistic variable is also used to denote its
membership function. In vact, they are quite different things; SLOW is
a members of discrete fuzzy set Speed, but Slow is also used to denote
its membership function.

We also have membership functions mapping numbers from the real line
onto grades of membership for fuzzy numbers. "Fuzzy_Two" is a
continuous fuzzy set with its own membership function, and could be
considered a linguistic variable with only one member. But there are
also continuous fuzzy sets that are do not conform to the usual
definition of a fuzzy number, i.e. that it be convex. These can result
from logical operations on fuzzy numbers, as when we aggregate
weighted membership functions prior to defuzzification.

In short, Scooter is confused because he has something to be confused
about.

William Siler