Re: fuzzy logic and probability:Simple Ans.

Ibrahim Larchie (larchiei@tuns.ca)
Fri, 12 Jul 1996 13:46:09 +0200


>: In article <4rfsju$pmb@ns1.nl.cis.philips.com>
T.W.J.Jakobs@nl.cis.philips.com
>: (Jakobs) writes:
>
>: >I was wondering if those so-called membership functions can
>: >be regarded as some kind of probability functions?
>: >I have to admit I don't know much about fuzzy logic, but
>: >at a first glance it seemed to me that there is a close
>: >relationship between fuzzy logic and probability theory.
>: >Am I right?

Yes! Mr. Jakobs, before your question gets lost in the debate
perhaps a simple answer to your apparently simple question might
be useful.
YES, there are lots of similarities between membership functions
as used in practical computation of fuzzy systems and probability
density functions ( c.f. the popular normal/gaussian density curve
with the 'bell- shaped ' membership functions).
However there are important differences between the two in many
respects. Perhaps a conceptual understanding of membership functions
could be based on the fact that they are a generalization of
characteristic functions.
I believe most of the confusion in applying these concepts arise
from inadequate grasp of the basics like the differences between
probability distribution and density functions,characteristic functions
and moment generating functions as they apply to
a) random variables, data and sets
b) imprecise or multivalued logic.
c) applicability to different types of data ( e.g purely sampled and
relatively well behaved data in closed system and times series or
other more complex data.

So a casual observation or ad-hoc application of principles is not
enough to make a judgement.
I hope this helps.

I. Larchie
Physiological Modeling Lab
TUNS, Halifax

"..science is not about the truth but reliable knowledge!"
(attr. to a Physicist Theologian in Australia)