: 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.
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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