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From: spg@uhura.neoucom.edu (Shiva P. Gautam)
Subject: Re: Fuzzy logic compared to probability
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References: <312B60FB.41C67EA6@colorado.edu> <4gh66g$r8@elna.ethz.ch> <4gktal$2ia@niaomi.iscm.ulst.ac.uk> <4gl2m3$2fo5@b.stat.purdue.edu>
Date: Tue, 27 Feb 1996 15:17:11 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.fuzzy:6837 sci.stat.math:9431

Herman Rubin (hrubin@b.stat.purdue.edu) wrote:
: In article <4gktal$2ia@niaomi.iscm.ulst.ac.uk>,
: JG.Campbell <jg.campbell@ulst.ac.uk> wrote:
: >poncet@isi.ee.ethz.ch (Andreas Poncet) wrote:
: >..Robert Dodier <dodier@colorado.edu> writes:

: >.. cut...

: >>Well, usually, in the papers about fuzzy logic, it is claimed that fuzzy
: >>membership functions are not to be mixed up with probabilities.
: >>But what kind of probabilities?  The arguments used are typically that

: >.. cut ...

: >I agree; mixing up the probabilities, with often more than one type of
: >probability in the same argument, is surely the most serious obstacle to such
: >enquiry. The points you raise are discussed in great detail -- and clarity, I
: >think -- in S.F. Thomas, Fuzziness & Probability, 1995, ACG Press; can be
: >ordered by e-mail from <brad.brown@acginc.com> approx. $30 +$10 p&p. To my mind
: >this is an important book. 

: This is where the problems arise.  Types of probability can, and should,
: be mixed.  

: I would never consider probability as relative frequency.  It is true
: that relative frequency is a probability measure, but this does not
: make it probability.  It is also true that, if one has independent
: events with exactly the same probability, that relative frequency 
: appraches that probability with probability one.  

:From the physical
: world, the fundamental probability is for the single event which cannot
: be repeated.

Sounds reasonable. But if we think on a similar line we should not punish a
criminal, because it is never the same person who committed the crime. The
time between criminal activity and punishment are not the same, in the
space time continium the person is not the same. Moreover, it is fruitless
to discuss the circumstances (by lawyers) in which the crime took place
because one can not exactly describe (repeat) the circumstance. In many
cases the jurors are taken to the plce of crime which is absolutely
absurd. Similarly, The house we paid for is not
our house right after we made the down payment. The person we were married
are not the same not only in time space continium but also all the cells
in the whole body will be replaced-practically he/she is a new person. etc.
Although you can not repeat an experiment exactly the same way what is
wrong with making inference from approaximations?

: As for mixing types of probability, what do you think the Bayesian
: approach, which has been present for more than two centuries, is?  
: -- 
: Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
: hrubin@stat.purdue.edu	 Phone: (317)494-6054	FAX: (317)494-0558
