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From: sthomas@decan.com (S. F. Thomas)
Subject: Re: Fuzzy vs. Probability: Just give it to me in plain English
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Date: Wed, 22 May 1996 21:04:49 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.fuzzy:7503 sci.stat.math:10777

Barry O'Sullivan (osullb@cs.ucc.ie) wrote:


: I think the easiest way to reconcile the differences between fuzzy 
: membership and probability is as follows. Probability is based on 
: randomness. Probability theory regards imprecision to be equated with
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: randomness. 
  ^^^^^^^^^^
This is a common misconception.  It is not so.

: On the otherhand, fuzziness is the type of imprecision 
: encountered when there does not exist a sharp transition between \
: membership and non-membership.

Yes.  Now consider the set of Bernoulli parameters which explain
the outcome on a single toss of say a thumb-tack for which we
wish to estimate the probability of it landing top down on a 
single toss.  Is there a sharp transition from membership to
non-membership for such a set?  If you agree the answer is no,
think about what that implies for the relationship between
probability and fuzzy.

: Kindest regards,
: 	Barry.

Regards,
S. F. Thomas
