# Re: Thomas' Fuzziness and Probability

From: Rodney Sparapani (rsparapa@mcw.edu)
Date: Thu Aug 23 2001 - 11:39:42 MET DST

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Andrzej Pownuk wrote:

> <SNIP>
> >
> > >When I see that knowledge
> > >of my students is related with probability,
> > >(For the same question I got
> > >different response.)
> > >then I doubt about their knowledge.
> >
> > This happens all the time.
>
> Students use different words
> in order to described the same fact.
> We can see when different answers
> are equivalent.
>
> What is the probability that John
> know the definition of kinetic energy?
>
> We can check this fact using two or three questions.
> If John know don't know the answer then
> we can ask him many times,
> but with the same result.
> John knows or doesn't know.
> We know that with probability 1.
> THERE IS NOTHING RANDOM
> in this situation.
> John can't invent definition
> of the kinetic energy in the classroom.
> (without additional source of information.)
>

I have to disagree. During my oral exam, I was asked the same question
2 times. The first time, I was only partially right and the second
time, after further reflection w/o reference to any other material,
I got it right. If I had been asked another time, I probably would
have got it right, but I could have easily confused myself again and got
it partially wrong. W/o proof, I submit that memory retrieval is a
random process if we are talking about a sufficiently complex detail.
This can be extended to rather elementary questions as I often forget
what the capitol of Kentucky is (same goes for the spelling of capitol).

>
> What is the probability that the food is fresh?
>
> I don't know haw to measure this fact,
> but the word "fresh" is connected with amount of bacteria
> and influence of chemical reactions.
> Both factors aren't random in concrete situation.
>

Perhaps it is just the difference between the way a statistician views
the world vs. an engineer; if so, this discussion may be futile. But,
freshness could be defined as: p(fresh)=1-p(eating this item causes
illness)

>
> What is the probability that the glass of water is full?
>
> The word "full" is connected with the following number
> m=(volume of water)/(volume of the glass)
> This is not random variable in concrete situation.
>

So m is not random, but unknown. Therefore, our determination of "full"
is random. At a canning/bottling operation, each container passes a
sensor to determine if it is "full". This sensor may employ fuzzy logic
perhaps, but the result is still probabilistic in nature, i.e. more
"full" cans are more likely to pass than less "full" cans.

>
> What is the probability that structure is damage?
>
> This is very difficult question which is connect
> with the number of microcrack and many another factors.
> The damage of the structure can be measured using different method
> but the damage of the structure is not random.
> (see for example Engineering Failure Analysis,
> Engineering Fracture Mechanics,
> International Journal of Fracture)
>

Maybe I'm mistaken, but I think your question is: what is the
probability that the structure will fail given what we know about how
"damaged" it is? If so, then this would be based on a model. And, I'm
assuming different models would be entertained that may give different
probabilities.

>
> There is nothing random in the in the height of John.
>

John's height is subject to random measurement/recording errors. For
John, the random component may or may not be ignorable.

>
> Andrzej Pownuk
>
> ---------------------------------------------
> MSc. Andrzej Pownuk
> Chair of Theoretical Mechanics
> Silesian University of Technology
> E-mail: pownuk@zeus.polsl.gliwice.pl
> URL: http://zeus.polsl.gliwice.pl/~pownuk
> ---------------------------------------------

```--
Rodney Sparapani              Medical College of Wisconsin
Sr. Biostatistician           Patient Care & Outcomes Research (PCOR)
rsparapa@mcw.edu              8701 Watertown Plank Rd., Rm. H2775
(414) 456-8786 (FAX: 6689)    PO Box 26509, Milwaukee, WI  53226-0509
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Andrzej Pownuk wrote:
<blockquote TYPE=CITE>&lt;SNIP>
<br>>
<br>> >When I see that knowledge
<br>> >of my students is related with probability,
<br>> >(For the same question I got
<br>> >different response.)
<br>> >then I doubt about their knowledge.
<br>>
<br>> This happens all the time.
<p>Students use different words
<br>in order to described the same fact.
<br>We can see when different answers
<br>are equivalent.
<p>What is the probability that John
<br>know the definition of kinetic energy?
<p>We can check this fact using two or three questions.
<br>If John know don't know the answer then
<br>we can ask him many times,
<br>but with the same result.
<br>John knows or doesn't know.
<br>We know that with probability 1.
<br>THERE IS NOTHING RANDOM
<br>in this situation.
<br>John can't invent definition
<br>of the kinetic energy in the classroom.
<br>&nbsp;</blockquote>
I have to disagree.&nbsp; During my oral exam, I&nbsp;was asked the same
question 2 times.&nbsp; The first time, I was only partially right and
the second time, after further reflection w/o reference to any other material,
time, I probably would have got it right, but I&nbsp;could have easily
confused myself again and got it partially wrong.&nbsp; W/o proof, I&nbsp;submit
that memory retrieval is a random process if we are talking about a sufficiently
complex detail.&nbsp; This can be extended to rather elementary questions
as I often forget what the capitol of Kentucky is (same goes for the spelling
of capitol).
<blockquote TYPE=CITE>&nbsp;
<br>What is the probability that the food is fresh?
<p>I don't know haw to measure this fact,
<br>but the word "fresh" is connected with amount of bacteria
<br>and influence of chemical reactions.
<br>Both factors aren't random in concrete situation.
<br>&nbsp;</blockquote>
Perhaps it is just the difference between the way a statistician views
the world vs. an engineer; if so, this discussion may be futile.&nbsp;
But, freshness could be defined as:&nbsp; p(fresh)=1-p(eating this item
causes illness)
<blockquote TYPE=CITE>&nbsp;
<br>What is the probability that the glass of water is full?
<p>The word "full" is connected with the following number
<br>m=(volume of water)/(volume of the glass)
<br>This is not random variable in concrete situation.
<br>&nbsp;</blockquote>
So m is not random, but unknown.&nbsp; Therefore, our determination of
"full" is random.&nbsp; At a canning/bottling operation, each container
passes a sensor to determine if it is "full".&nbsp; This sensor may employ
fuzzy logic perhaps, but the result is still probabilistic in nature, i.e.
more "full" cans are more likely to pass than less "full" cans.
<blockquote TYPE=CITE>&nbsp;
<br>What is the probability that structure is damage?
<p>This is very difficult question which is connect
<br>with the number of microcrack and many another factors.
<br>The damage of the structure can be measured using different method
<br>but the damage of the structure is not random.
<br>(see for example Engineering Failure Analysis,
<br>Engineering Fracture Mechanics,
<br>International Journal of Fracture)
<br>&nbsp;</blockquote>
Maybe I'm mistaken, but I think your question is:&nbsp; what is the probability
that the structure will fail given what we know about how "damaged" it
is?&nbsp; If so, then this would be based on a model.&nbsp; And, I'm assuming
different models would be entertained that may give different probabilities.
<blockquote TYPE=CITE>&nbsp;
<br>There is nothing random in the in the height of John.
<br>&nbsp;</blockquote>
John's height is subject to random measurement/recording errors.&nbsp;
For John, the random component may or may not be ignorable.
<blockquote TYPE=CITE>&nbsp;
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Andrzej Pownuk
<p>---------------------------------------------
<br>MSc. Andrzej Pownuk
<br>Chair of Theoretical Mechanics
<br>Silesian University of Technology
<br>E-mail: pownuk@zeus.polsl.gliwice.pl
<br>URL: <a href="http://zeus.polsl.gliwice.pl/~pownuk">http://zeus.polsl.gliwice.pl/~pownuk>
<br>---------------------------------------------</blockquote>
<pre>--&nbsp;
Rodney Sparapani&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Medical College of Wisconsin
Sr. Biostatistician&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Patient Care &amp; Outcomes Research (PCOR)
rsparapa@mcw.edu&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 8701 Watertown Plank Rd., Rm. H2775
(414) 456-8786 (FAX: 6689)&nbsp;&nbsp;&nbsp; PO Box 26509, Milwaukee, WI&nbsp; 53226-0509</pre>
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