The problem with using many, many membership functions is simply this: a
membership function by itself simply defines one semantic partitioning of the
variables Universe of Discourse. A MF onlyparticipates in a model when we have
a rule that descibes the mdoel behavior through the interaction of these MF.
So..if we define 10,000 MF (to pick some really absurd number) then we would
need at least 10,000 rules to describe the state of the model for each MF. So
if I have three variables with fifteen MF's each, then the rules are 5**15 or
approx 3.05x10**10. Which is alot. ;-)
Of course Bill Comb's method of rule Union side steps the exponential growth of
rules with variables, but the basic problem still exists.
The comment about "fuzzy logic is supposed to be used in an environment with
uncertainty in which it is not possible or too difficult to get all
input-output data" is just plain wrong.
Almost as wrong as the statement about "a good enough solution."
'Course, these are just my opinions.
Earl
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