I realize than many or most fuzzy persons share your viewpoint here, but I do
not. Both probability distributions and membership functions look from
different vantage points ar pretty much the same thing - uncertain numbers,
whatever the cause of the uncertainty may be. A very few persons have worked
seriously on the relationship between the two, which I think is unfortunate.
There is, in any event, a quick (if incomplete and inaccurate) answer to the
question. Probability density functions have area one; fuzzy numbers and
membership functions usually have max value one. Simply normalize the
probability distribution to a max value of one, and there is your fuzzy number
or membership function. If the probability distribution is discrete, do the
same thing, and there is your discrete fuzzy set.
The question of the circumstances under which that simple answer is wrong is
interesting, and comments on this would be welcome. Am I wide open?
William Siler
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