Not true. If we are dealing with continuous information, and we "force" it into
a discrete fuzzy set, the information now available includes not only the
grades of membership of the discrete fuzzy set members, but also their
membership functions. It is a piece of cake to set up reversible fuzzification,
so that when we defuzzify a discrete fuzzy set we get back precisely (within
the granularization imposed by finite computer word length) the number we just
put in. There is no loss of information at all. True, we are dealing with a
finite range, but that can be handled by adding fuzzy set members "small-error"
and "tall-error" if we wish.
>>"I think I can see the real advantage of fuzzy set theory. In traditional
>>set theory if a man grew by just 1/4 inch he could fall into a completely
>>different set. Fuzzy set theory would overcome such a clear-cut, abrupt
>>change with a gradual smoothing effect."
>
If you want to use "traditional" maths, fine, go ahead. But then we lose the
advantage of expressing rules in term of words which are comprehensible to a
non-mathematician. That is the real advantage of fuzzy; we can reason in the
way humans who are not Mathematicians do. Since I'm a biologist, I consider
this to be an enormous advantage.
>Fuzzy logic is solving a problem it created in the first place.
A problem? Not in my book. I love it.
>In traditional maths, for this type of problem we would not try to split up a
>set of real numbers into subsets in the first place. We already have far
>more information contained in the actual height of a man, say 6' 0" than we
>would if we said that he was in the set 'tall'.
As said above, not true. When we fuzzify, we have grades of membership in an
entire discrete fuzzy set, not just in "tall" "tall" is only one member of a
discrete fuzzy set.
>Note that 6' 0" also conveys far more information than 'a member of the fuzzy
>set 'tall' with a degree of membership of 0.8', and that it even requires less
>storage space in terms of memory.
Again as said above, 6' 0' conveys no more information than the discrete fuzzy
set say "size" with members say {tiney, short, medium, tall, very-tall}. It is
true that 6' 0" requires less storage space, but in these days who cares?
So, Martin, I think your conversation with your imaginary friendis based on a
false assumption that there is a loss of information when fuzzifying takes
place.
William Siler
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