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From: mackw@bytex.com
Subject: Re: Fuzzy theory or probability theory? 
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In article <94Dec5.200110edt.830@neuron.ai.toronto.edu>, 
<radford@cs.toronto.edu> writes:
> >In summary, if probability information is available or easily 
attainable, 
> >use it to determine membership sets.  The advantage of fuzzy logic is 
in 
> >cases where you do not want to obtain this data to this level of 
> >precision, you do not have to give up and say the problem is 
impossible 
> >to solve.  
> 
> You don't have to give up when using probability either.  The
> difference is that when using probability, which has a well-defined
> meaning, you may start to wonder whether your simplifying assumptions
> have rendered your conclusions worthless as far as the real world
> goes.  With fuzzy logic, it seems that such doubts are easily
> suppressed, since the statements have no well-defined semantics
> anyway.  It is only in the final use of the results that a meaning is
> imposed, in ad hoc fashion, after the stage where doubt might have
> been possible.

If people were not giving up when faced with the prospect of using 
probability to solve certain problems, how do you explain the fuzzy logic 
products which are now solving previously unsolved problems?  Often they 
are using the same microprocessors and the same sensors as before and I 
do not believe the developers have had a sudden increase in IQ.  The 
change is a different way of processing the information - fuzzy logic.

Also, to be fair, we should also consider the simplifying assumptions 
which go into probability.  (1) Faced with a large number of variables, 
most are eliminated as "insignficant" to get to a manageable number.
(2) We then take random (or not so random) samples which we hope 
represent the target population.  (3) We combine samples based on what 
looks right into sets.  (4) We graph these sets and eyeball them to 
determine if they fit into a normal distribution (or sometimes we don't 
even look and assume a normal distribution).  (5) We then calculate 
averages and standard distributions and generate a normal distribution 
curve which is assumed to represent the actual population.

This is not a diatribe against probability.  I find probability extremely 
useful, but it does have practical limitations.  Yes, fuzzy logic uses 
some approximations and it assumes that these approximations do not 
significantly affect the result, but it is unfair to say the same thing 
does not occur with probability.  Simplification is necessary to solve 
complex problems.  And it must be noted that for at least some problems 
where both a probabilistic approach and a fuzzy logic approach have been 
used, the fuzzy logic approach worked better.  I'm sure there are also 
cases where the fuzzy logic approach may have worked worse, but the point 
is there seems to be a certain class of problems that fuzzy logic solves 
that were not solved or not solved as well using probability.

Use the appropriate tool for the problem!

Wayne Mack

