> Okay, I've read scores of intros, FAQs, etc. on Fuzzy Logic, and STILL,
> although everyone insists that this is true, no one has been able to clarify
> HOW exactly fuzzy differs from probability. Can anyone supply an
example of a
> problem? How exactly are these complex membership functions being
derived, if
> not by mathematical probability? I'm not deriding fuzzy logic, I'm seriously
> just a newcomer who wants to know more. Any help would be appreciated.
>
Try this:
1. Fuzziness is deterministic uncertainty -- probability is nondeterministic.
2. Probabilistic uncertainty dissipates with increasing number of
occurrences -- fuzziness does not.
3. Fuzziness describes event ambiguity -- probability describes event
occurrence. Whether an event occurs is random. The degree to which it
occurs is fuzzy.
As an example, consider the range of height from 0 to 12 feet. We might
say that anything over 7 feet is definitely tall and that anything under 5
feet is definitely not tall. Therefore anything between 5 feet and 7 feet
is somewhat tall (i.e. a fuzzy subset).
The degree of belief in the set tall assigned to a particular height, say
5.5 feet will never change -- it is a function of the particular choice
(expert experience) in the membership function used to describe our
somewhat tall membership function.
Probability on the other hand is a matter of trying to predict or guess
where a particular population sample will fall on the graph. You might use
a standard distribution function to predict how many people out of a given
sample might be under 5 feet, over 7 feet, or between 5 and 7 feet.
Regardless of what the laws of probability say about how many members of a
population might fall in the range of 5 feet to 7 feet, it has nothing to
do with the degree of belief that we attached to the particular point of
5.5 feet in the "somewhat tall" fuzzy subset (or any other point in that
subset).
Hope this helps -- Edgar