Re: Fuzzy vs. Probability: Just give it to me in plain English

S. F. Thomas (sthomas@decan.com)
Fri, 24 May 1996 16:18:16 +0200


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