Quote by Ray12
One thing I've wondered for quite some time, and looked for, but not found anything I consider adequate is whether there is a theory of probability based on Zadeh's fuzzy set theory.

One of the strengths of fuzzy set theory is that it is not a probability theory. An element of a fuzzy set that has a 0.7 degree of membership in it, does not have a 0.7 probability of being in the set and a 0.3 probability of not being in the set. It has a definite degree of membership equal to 0.7. So, for example, a house might have a 0.7 degree of membership in the set of "colonial style houses". If you treat the degree of membership as something determined by a random variable, the you can ask questions like "what is the probability that a randomly selected house has a degree of membership in the set of "colonial style houses" that is between 0.7 and 0.75? Such things are handled by ordinary probability theory.
So it isn't clear what one would mean by "a theory of probability based on Zadeh's fuzzy set theory" because fuzzy set membership does not resemble probability and ordinary probability theory can be applied to fuzzy set membership.
Did you have specific goals or ideas for a generalization of probability theory that somehow incorporates fuzzy sets in a new way? It would be interesting to discuss.