To assert that a normal distribution characterizes a numeric random variable
subject to a large number of small errors amounts to a tautology, parameterized
perhaps as a mean and variance. However, I can (and often do) characterize that
same variable as a bell-shaped fuzzy number, paramaterized perhaps as central
value and a hedge "roughly". There is no vagueness here, just an uncertainty as
to precise value. In an expert system, "roughly 2" is a heck of a lot more
useful than "2 +/- 25%".
A list of the kinds of uncertainty which can be fruitfully represented by fuzzy
quantities (e.g. truth values of scalars, fuzzy numbers, membership functions,
truth values of rules, truth values of members of a discrete fuzzy set,...)
would probably be quite long. If I'm not sure that a car is a Ford or a
Chevrolet, that uncertainty is easily represented by the grades of membership
in a discrete fuzzy set of car makes, for example.
I'm not sure what latitude FRIL offers in the kinds of things which can be
represented by fuzzy quantities, but I surely hope it covers more than vague
definitions.
William Siler
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