Re: justifying fuzzy sets

["Peter L. Schuerman" <plschuerman@UCDAVIS.EDU>]

On Thu, 23 Nov 1995, Steven M. Belknap wrote:

> If I have a hammer and I use the hammer as a keyboard entry device, I will
> likely meet with unfavorable results. This does not mean that hammers are
> not useful.

Similarly, formal logic is only useful when used correctly.  You see my
point?  Here's how the analysis *should* go.

I used a hammer as a keyboard entry device.
Compared to using my fingers, the results were not good.
(criteria: ease-of-effort, keyboard damage, etc.)
Therefore, hammers are not as good as fingers for making keyboard entries.

You see, you used the word "unfavorable."  But what is the standard of
reference?  You left it out, but I assume it was "manual entry."  And of
couse, the conclusion is not that hammers are "not useful" but rather
that hammers are not useful for this particular job.

Just because you are making poor use of formal logic and common sense
doesn't mean that they can't suffice for analysis, in another person's
more competent usage.

> I used fuzzy sets in this way in some software I wrote to aid physician
> decision-making about treating high blood pressure. My model used 170
> inputs, about half were fuzzy inputs. (Pulse rate, Systolic Blood Pressure,
> Diastolic Blood Pressure, Serum Glucose, subjective sense of wellness,
> exercise tolerance, etc.) I then took a few dozen individual patient cases
> and (using myself as the "expert") choose outputs. I used this output to
> train the fuzzy neural net to simulate my choices. This involved using
> fuzzy logic to discover the relative importance of different factors, (many
> of which could be discarded without affecting the behavior of the model.)
> This turns out to be quite effective and useful.

This is just vector-sum calculation.  Not really a new idea, except that
you are including subjective data as well as objective data.

> >OK, describe what I mean when I say that a restaurant was a 4.5 on a
> >restaurant-scale of 0 to 8.
>
> If you ever come to Chicago perhaps we can go to one of our many fine
> restarants to further discuss the relative value of various logical
> systems. But which restaurant? There is a magazine called Chicago Magazine
> which rates the restaurants here. They use an 8 point scale expressed as
> stars and half stars. A second scale evaluates cost. In my twenty years of
> using this guide, I have been impressed with the utility of this guide.

Yes, but what is a 4.5 on a scale of 0 to 8?  I mean, really... what
picture does it create in your mind?  What do you *really* know about the
restaurant now that I've communicated this information to you.

> Obviously, Korean food is much different than nouelle cuisine, and there
> are many other objective & subjective factors.

To say the least.

> Several hundred thousand
> people use this guide every month; a favorable rating can fill a
> restaurant, and unfavorable rating can empty it. So here we all are in
> Chicago using the system you claim is of no value. We Chicagoans must be an
> awfully foolhardy lot.

If you say so.  But anyway, the problem is that the numbers aren't being
used as numbers (in other words, a 3 restaurant isn't really 2 times
worse than a 6 restaurant), they're just being used as symbols for words
like "awful", "good", "bad", "wonderful" etc.  So why pretend that the
evaluation is somehow mathematical, when it is only subjective?

> Why do you find it so difficult to believe that meaningful
> communication about continuously varying quantities can occur?

Some concepts are continuous and can be described by number.  Voltage.
Intensity.  Length.  Weight.  But face it, you can't weigh an idea, you
can't measure an opinion and you can't determine the circumference of a
dream.  If someone wants to use numbers to describe an experience, that's
fine, but the numbers are not being used as *numbers*.  They are being
used as symbolic representatives for adjectives.  I bet that any of your
patients could give a description, in words, of what 4-pain is, and what
8-pain is, but to conclude that 8-pain is exactly twice as "bad" as
4-pain is absurd... pain is a complex phenomenon, and not numerical in a
simple, scalar fashion.

> >Discrete logics do model human thinking quite well
>
> Do you have some evidence to support this assertion? It is at variance with
> my own observations and with the scientific literature.

The people who support this idea are often very unaware of how embedded
they are in language.  For instance, one might ask the question, "What did
the ancient Greeks think about love?"  The answer is, not much... and if
they had heard about it, it just would have been a foreign word to them.
"Love" is an abstraction that is derived from our culture.  The Greeks
certainly seem to have had concepts *related* to love, but the ideas are
not portable between cultures.  It would be like a Hawaiian scholar asking
the question, "How do the French conceptualize aloha?"  Well, they
don't.  Now, with regard to the assertion that fuzzy logic parallels
human thought, the problem is that people redefine words numerically
(bald goes from "lacking head hair" to "a numerically-defined expression
describing hair on the head".  Then, they ask, "How do people
conceptualize baldness (given that it is, in fact, a numerically-defined
expression)."  Notice that now, we're not even talking about how humans
think, we're talking about how computers would model how humans think.
It's no wonder that these researchers find parallels between human
thought and fuzzy logic!

> >Bob is tall.
> >
> >True or false?  You can't say, not because the subject is "fuzzy" but
> >because the frame of reference isn't stated.
>
> O.K. My frame of reference is US Men. Bob is 6'1" Now that I have given you
> a frame of reference and measurement, proceed with your analysis...

Still not enough information.  What height is the cutoff point for tall?
We need a criterion.  *All* evaluations need criteria.  It's inherent in
the concept of evaluation.

> >Fuzzy logic encourages one to stop analyzing, by oversimplifying.
>
> I return to my hammer example. Just because someone uses a hammer foolishly
> does not diminish the utility of hammers in competent hands.

Your example is good, because it was a perfect example of
oversimplifying.  A hammer is useless because you can't type with it?
Perhaps that goes *beyond* oversimplification...

> >Yes, one of the statements is, upon analysis, meaningless.  I've already
> >explained that truth isn't scalar.
>
> Yet this sort of statement is part of everyday discourse! How frustrated
> you must be when so many of the people around you make meaningless
> statements. I begin to understand the source of your linguistic nihilism.
> :-)

Not so.  One simply translates.  On a scale of 1 to 10, 1 means "not much"
and 10 means "a lot" and so forth.  However, you don't treat these numbers
as numbers.  You can't do math with them.  You can't do statistics with
them.  Everyone realizes this, except the fuzzy logic folks who think that
a person who is a "10" is twice as good looking as a person who is a "5".

Peter Schuerman                                    plschuerman@ucdavis.edu
                        Co-editor, SPECTRA Online
          for back issues: http://www.well.com/user/phandaal/