Does Godel's Incompleteness Theorem Apply to Fuzzy Sets?

[Eidos]

Hello all

Does Godel's incompleteness theorem still hold true for fuzzy sets?

My feeling is that it doesn't since the http://en.wikipedia.org/wiki/Law_of_excluded_middle" no longer applies.

Is this reasoning correct?

 

[Hurkyl]

When formalized, fuzzy set theory is a formal theories written in classical first-order Boolean logic.

That the arithmetic of fuzzy sets doesn't obey the law of the excluded middle has no bearing on the fact that the classical logic we use to reason about them does.