justifying fuzzy sets

["Steven M. Belknap" <sbelknap@UIC.EDU>]

We are getting rather far afield of lojban, but I will post this on the
lojban list because of the volume of direct email postings I have gotten on
lojban and fuzzy logic. I would encourage those who wrote me to post those
portions of their discussions regarding lojban & fuzzy logic direct to the
list. Peter seems skeptical about whether fuzzy logic has any value at all,
and therefore seems to be arguing that there should be no formalism in
lojban for fuzzy logic utterances.

>Peter Schuerman wrote:

>With regard to this discussion:
>
>Fuzzy logic is an attempt to quantify words and experiences which possess
>the quality of "continuousness."  For instance, "sound" can be measured
>across a continuum.  It can be measured as the intensity of vibration, or
>as frequency, etc.  However, "loudness" or "quietness" cannot be measured.
>Why not?  Because these are subjective, and there is no fixed criteria.
>What is loud for one person is not necessarily loud for another.  Even if
>we can get many, many people to agree that "greater than X intensity" is
>"loud" and that "less than X intensity" is "not loud" this doesn't change
>the fact that the determination is subjective, and that you are actually
>measuring intensity and *calling* it loudness.
>
>Another example: happiness.  You can measure brainwaves, levels of
>endorphins, heartrate, etc. all you want.  You can correlate certain body
>states with claims (by the person being studied) that they are happy.  So
>what?  You are still only measuring body functions, not happiness.
>Correlation is not identity, or so my statistics prof always used to say.

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.
>
>> I am not redefining the word bald. American Heritage Dictionary defines
>> bald as "lacking hair on the head" Dictionaries are generally agnostic on
>> the question of whether a discrete or continuous logic is being used.
>> Certainly the AHD definition of bald does not imply a two-valued logic.
>
>And it sure as hell doesn't imply the idea that you can be 0.32-bald, or
>6-bald, or any other such nonsense.  All it implies is that baldness is a
>lack of hair, with "lack" being judged by personal aesthetics.  If you
>want to count hairs to determine whether someone is bald, feel free, but
>you *know* that this is not how people *really* make such judgements.
>And, even if you do decide to put baldness on some sort of numerical
>scale, you know it's no better than a system where you say
>"not-bald/sorta-bald/kinda-bald/nearly-bald/bald/really bald/very bald"
>(that is, the distinctions carry no real information except that the
>speaker is being vague.)
>
Neither does the AHD definition of bald imply a two-valued logic. As I
wrote earlier, the dictionary definition is silent as to logical system and
set structure. Fuzzy logic and fuzzy sets may be used by speaker-listener
pairs (if both agree to do so) with no change to the definition of bald.

>> >> Although it might sound strange in English, we could describe
>> >> the baldness of the men on, (for example) a 0 to 7 scale.
>> >
>> >It's not strange, it's just pretense.  Scalar logic is just a way to
>> >dress up subjective interpretations as objective determinations.
>>
>> I'm willing to be thought pretentious. I would point ought that the
>> rational numbers have proven to be quite useful in other areas. Perhaps
>> they are useful in logic.
>
>I would love to see an example of how numbers can illuminate logical
>analysis.
>

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.

>> >No one will understand what 6-baldness is unless you show them.  For all
>> >the usefulness of this linguistic construction, you might as well point
>> >and grunt.  :)
>>
>> On what basis do you make this assertion?
>
>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.
Obviously, Korean food is much different than nouelle cuisine, and there
are many other objective & subjective factors. 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.
>
>> I often use a 1 to 10 scale with patients & experimental
>> subjects, and they seem to understand what I mean, and provide useful,
>> reproducible responses when we have objectively quantified them.
>
>Great!  By all means, use them!  :) When talking to a doctor about pain, I
>am sure the patients learn to get the doctor to focus on certain pains
>more than others by careful application of the numbers.  This could also
>be achieved by having the patient make simple statements, but doctors
>don't tend to like patients to diagnose themselves... it's much better to
>make a numerical guessing game out of it.

Sounds like you and your physician do not see eye-to-eye. Sorry to hear that.

>
>Example 1.
>Patient: Doc, I need some Tylenol with codeine for my arm.  It hurts!
>Doctor: (irritated) So when did *you* go to med school?
>Patient: ummm... I mean, I think there's something wrong with my arm.
>Doctor: Come back tomorrow if it's worse.
>
>Example 2.
>Patient: Doc, my arm really hurts... can you make it stop?
>Doctor:  Well, hmmm... I don't know.  How much does it hurt?
>Patient: (thinking a moment) An 8?
>Doctor: That's nearly a ten!  Well, here's your Tylenol with codeine!
>Patient: (to himself) Cool!
>
>(okay, so I'm in a 7-silly mood... just ignore those, please :)
>
>Anyway, for a patient to rank a pain higher than any others, he's simply
>saying "this is the pain that's bothering me most."  The highest pain
>value probably is a good indicator of how "tough" the patient is... a
>tough, macho guy is hardly going to admit to having "10" pain even if his
>leg is broken!
>

Recently I had a patient with metastatic breast cancer who was admitted for
intractable chest pain. There are many misconceptions about pain. This
patient was able to talk on the phone, sleep, smoke cigarettes, etc. Some
might think she was not in pain. Yet, I have seen this situation many times
in other patients. I believed she was in pain.

I asked this woman to rate the severity of her pain as we adjusted her pain
medication. Initially we used a drug-delivery system which provided a
continuous, high concentration of narcotic. Surprisingly, this was not very
effective. We had to push the dose to the point of toxicity. Then we
noticed something interesting. Her 1 to 10 ratings of pain were markedly
more episodic than is usually the case, spiking up into the 7 to 9 range,
so we changed to a subcutaneous patient controlled analgesia system, in
which she could squirt herself with narcotic when her pain was severe and
forego the narcotic when it wasn't that bad. But she also had baseline pain
around 3. So we gave a very low dose constant infusion of narcotic also
This worked very well. The total daily dose of narcotic with this dosing
regimen was 1/3 of the total daily dose of narcotic she was originally
getting, she had better pain control, and less nausea and other adverse
effects.

There are many other considerations in pain control. This patient turned
out to have a bony metastasis to her arm, which was causing her chest pain!
(Things in medicine sometimes just aren't simple, and strange things
happen. Everybody's a little different.) We used radiation therapy and
ibuprofen (good choice for bone pain) to treat this pain, and she is now
off of patient controlled analgesia, and has negligible pain.

Some patients refuse to use the 1-10 scheme. So then I don't use it either.
But most people seem to intuitively understand what I mean, and this
approach is often a helpful one.

>> You provide no explanation of why you think fuzzy definitions are not
>> useful in resolving the obvious absurdity of a hill suddenly turning into a
>> mountain. Claiming, "its all subjective" seems nihilistic to me.
>
>All I'm saying is that any description that anyone makes is based on
>their own criteria.  Is that so hard to believe?
>

No. Why do you find it so difficult to believe that meaningful
communication about continuously varying quantities can occur?

>> I believe
>> it may be possible to improve understanding among people by enriching
>> language in certain ways, such as a better understanding of fuzzy sets, and
>> a better understanding of how people actually think. My hypothesis is that
>> discrete logics do not model human thinking very well.
>
>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.

>but tend to fail
>when linguistically-unaware people use it.

I am less interested in the experience of professors of linguistics
communicating with each other than in the experience of the vox populi.

>This is because logic is only
>as good as the material it starts with... garbage in, garbage out.  If
>someone insists that such words as tall, bald and beautiful have some
>sort of objective definitions, and then uses these words in statements
>which are then logically analyzed, there will be some real problems
>unless the statements are broken down into their actual meanings.
>Consider this:
>
>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...

>
>> A squirrel which weighs 2.3 kgs does not know he weighs 2.3 kgs. People who
>> accurately use fuzzy sets in their daily discourse may not consciously use
>> numerical criteria. Yet such criteria may accurately model their thinking
>> and discourse.
>
>A numerical basis for consciousness?  How would this work... would you
>measure qualities such as love, greed and wistfulness by the number of
>neurons firing, or the rate of acetylcholine synthesis in certain
>defined regions of the brain?
>
>Of course, there *may* be numerical underpinnings for such things, but the
>number of consciousness-elements involved in just "having an opinion about
>something" is probably staggering, and if so, a 1-to-10 scale wouldn't
>even be *remotely* adequate.

And the number of molecules in the sea is staggering, yet we can estimate
their number with a small expenditure of effort...

>
>> And providing a mechanism for describing their intuitive
>> understanding in a fuzzy way may be useful, even if such constructs are
>> unwieldy in natlangs.
>
>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.

>
>> >> You are claiming that all such
>> >> statements must be metareferences, which does not seem reasonable to me.
>> >
>> >Why not?
>> >
>> Sam is somewhat bald.
>> It is somewhat true that Sam is bald.
>>
>> These are different statements, with different meanings. QED
>
>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.
:-)

For many centuries people claimed that the equation x^2+1=0 was
meaningless. So it goes.

la stivn


Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria

email: sbelknap@uic.edu
Voice: 309/671-3403
Fax:   309/671-8413