[pedrosorio]

"you can't have a temperature that is 80% hot AND 80% cold. This problem becomes even more apparent as you increase the number of states"

I don't see why this is an issue. You can also define each of the states as its own binary random variable and then the probabilities of two states conditioned on the temperature can add up to more than 1.

I thought your original post was meant to explain a practical application of fuzzy theory and how it differs from probability theory. Perhaps there is another example that better illustrates how fuzzy theory simplifies a problem where using probability theory would be messy / impossible?

[thanatropism]

> You can also define each of the states as its own binary random variable and then the probabilities of two states conditioned on the temperature can add up to more than 1.

Yes, but then you're defining a probability distribution over the space of fuzzy states.