Path: utzoo!attcan!uunet!husc6!bloom-beacon!gatech!udel!rochester!ur-tut!sunybcs!bingvaxu!vu0112
From: vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn)
Newsgroups: comp.ai
Subject: Re: Fuzzy systems theory was (Re: Alternative to Probability)
Summary: Hey, wet this, buddy.  ;->
Keywords: fuzzy, logic, realism
Message-ID: <1213@bingvaxu.cc.binghamton.edu>
Date: 18 May 88 05:25:51 GMT
References: <4134@super.upenn.edu> <3200014@uiucdcsm> <1484@pt.cs.cmu.edu> <1196@bingvaxu.cc.binghamton.edu> <183@proxftl.UUCP>
Reply-To: vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn)
Organization: SUNY Binghamton, NY
Lines: 92

In article <183@proxftl.UUCP> bill@proxftl.UUCP (T. William Wells) writes:
>4/5/88
>
>Dear Editor:
>
>The article "When Facts Get Fuzzy", BYTE, April 1988, p.  285,
>contains fuzziness of its own: philosophical fuzziness.

I saw the article, but only examined it enough to understand that it is
very elementary.

You object that Fuzzy measures are necessarily subjective, that is,
'partly cloudy' cannot be an attribute of the sky, only of our judgement
of the sky.  In this case you are right, but what is critical to
understand is that it is *also* true of crisp (non-fuzzy measures).  For
example, I say "What's that smell," you say, "I don't smell anything."
Here there is no ambiguity about the smell (it is either there or not),
but clearly there is uncertainty as to whether the smell exists or not. 
Is it *real* uncertainty (maybe it does, maybe it doesn't) or is it this
terrible *subjective* uncertainty (maybe I'm wrong, or you're wrong). 
The truth is that we might never be able to know.  This basic epistemic
principle is also a natural consequence of moving to a quantum physical
model, which incorporates objective uncertainty at its base. 

>A philosophically accurate (at least to a Realist) statement is:
>"partly cloudy" is the form in which some particular person
>perceives the sky when the sky contains clouds in certain
>configurations.  People can say "partly cloudy" and be understood
>by others because the configurations which people see as "partly
>cloudy" are usually the same.

So what? All our theories of nature are built from common observation,
and any common observation can be perceived differently by different
people, not just ambiguous ones.  Does that make it "philosophically
inaccurate?"

>Consider the statement "I see that the sky is partly cloudy."
>There is no ambiguity there; either I do see this or I do not and
>the statement is either true or false as a consequence.  It might
>be the case that sometimes, given the same sky, I would report it
>as partly cloudy or not and one could measure a probability, but
>that probability is an attribute derived from myself, not from
>the sky alone.
>
>The only way to fix the ambiguity, without making the error of
>attributing "partly cloudy" to the sky, is to make use of
>measurements of the density and distribution of clouds in the
>sky; these being attributes of the sky and independent of who is
>looking at it.  After having done this one can then give a
>rigorous definition of "partly cloudy" and any statement about
>the cloudiness of the sky can be validated by using this
>definition and without reference to who is making it.

You very accurately describe some of the important philosophical
problems involved in the determination of fuzzy set membership grades. 
Your former method is subjective, the latter objective.  As I mentioned
above, this distinction is useful and necessary: it is critical to know
when to act subjectively, when objectively.  Frequently we move from one
to the other, using one to construct the other.  Neither invalidates the
other, or is "bad science," or "bad philosophy."

>The same kind of reasoning applies to the idea of "young".  If
>one specifies WHO thinks that someone is young, the ambiguity
>goes away; and if one does not, all you can get is a statistic
>which indicates what fraction of some group of people think that
>a person is young.

The real question is whether youthfulness is a natural kind.  If so,
does it have a crisp definition or not? If not, then it *is* a fuzzy
object, no matter how we see it.  For example, electrons are natural
kinds, but there is a fuzzy boundary between them and the rest of the
universe.  The position of the particle is ambiguous.  This is objective
amiguity.  On the other hand, the roll of the die is also ambiguous, but
is deterministic and chaotic.  Here the ambiguity is subjective. 

>Because fuzzy logic is based on a fallacy (the assignment of set
>membership based on a relationship, while disregarding the
>thing(s) being related to), any conclusion derived by the use of
>fuzzy logic is invalid.  Cases where it appears to work are sheer
>dumb luck.

Is this kind of polemic really necessary? Anyway, your statement appears
unsubstantiated, and unrelated to the flow of your previous argument. 
Please explicate the nature of the fallacy, the 'relationship' alluded
to, etc., before denigrating a field you seem to have only a naive
familiarity with. 

-- 
O---------------------------------------------------------------------->
| Cliff Joslyn, Cybernetician at Large
| Systems Science, SUNY Binghamton, vu0112@bingvaxu.cc.binghamton.edu
V All the world is biscuit shaped. . .