# Re: Thomas' Fuzziness and Probability

From: Andrzej Pownuk (pownuk@zeus.polsl.gliwice.pl)
Date: Wed Aug 22 2001 - 20:48:57 MET DST

• Next message: S. F. Thomas: "Re: Thomas' Fuzziness and Probability"

>>> >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.

>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).

I don't know how work our brain.
Maybe when information is complicated
and connected with another part of our knowledge
there is some random phenomena in our thinking.
The connections are random.
This is probably true,
but that if we don't know something
which is not a logical conclusion
we can't guess this.

I remember the Planc's constant or not.
There is nothing random in this fact.
(except sclerosis which is random)

Our knowledge is very complicated,
but I can't agree that my memory is random process.
(Maybe when I'm drunk.)

>>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)

We can define the word fresh in two different ways:

a) m(fresh)=f(amount of bacteria)
b) p(fresh)= 1-p(eating this item causes illness)

Let us consider that all people in the city are the same.

As far as I know, if somebody is ill then
the amount of bad bacteria have to
be grater than some level.

Now we can compare both measures.

m(fresh) p(fresh)
0 1
0.1 1
0.2 1
0.3 1
0.4 1
0.5 1
0.6 0
0.7 0
0.8 0
0.9 0
1 0

I don't think that p(fresh) is a good description of the word "fresh".
If we change people in the city then p(fresh) also change.
m(fresh) is constant and depend only on food.

What happened when somebody
will eat this food is a different problem.

>>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.

Sorry for may poor language skills.
I this case I assumed that we know the amount of water.

>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.

When we apply sensor we use different definition
of the word "full".

m1(amount of water)=0 if ( m(amount of water) < m0 )
m1(amount of water)=1 if ( m(amount of water) >= m0 )

where m(amount of water)= (volume of water)/(volume of the glass)

My question is the following.
Where in this definition we can apply probability?
What is random in definition of function m1 or m?

I think that the result of functions
m and m1 are deterministic.

>>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.

You described reliability of structures.
Reliability and damage are two different things.

In theory of reliability we ask
"how often structure fails"
"what is state of the structure"
or
"how many cracks has the structure"
(this is not exact definition.)

>>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.

I think that in this case measurement error are very small,
but if we consider quantum mechanics ...

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
---------------------------------------------

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