What is the difference between probability and fuzzy logic?

Probability, which ranges from 0.0 to 1.0, is used to gauge the likelihood that some particular, well-defined state is or will be the case, under conditions of ignorance or chance. For instance: a fair coin has a 50% probability of coming up heads. Note that: 1. we do not know the outcome ahead of time, due to chance and 2. there are only two, clearly-defined states: "heads" and "tails".

Fuzzy set membership, which also ranges from 0.0 to 1.0, indicates the degree to which an individual case or circumstance belongs to a fuzzy set. Here, values between 0.0 and 1.0 are a result of the inherently imprecise nature of the definition of the fuzzy set, not ignorance or chance.

To illustrate the difference, consider this scenario: Bob is in a house with two adjacent rooms: the kitchen and the dining room. In many cases, Bob's status within the set of things "in the kitchen" is completely plain: he's either "in the kitchen" or "not in the kitchen". What about when Bob stands in the doorway? He may be considered "partially in the kitchen". Quantifying this partial state yields a fuzzy set membership. With only his little toe in the dining room, we might say Bob is 0.99 "in the kitchen", for instance.

No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway. Fuzzy sets are based on vague definitions of sets, not randomness.

Here are links to some reasonably good introductory material on fuzzy logic:

http://www.austinlinks.com/Fuzzy/overview.html
http://www.ncst.ernet.in/education/apgdst/aifac/aicontent/fuzzy/fuzzy.pdf
http://www.fpk.tu-berlin.de/~anderl/epsilon/fuzzyintro4.pdf
http://www.phys.ufl.edu/docs/matlab/pdf_doc/fuzzy/fuzzy_tb.pdf
http://www.faqs.org/faqs/fuzzy-logic/part1/
http://www.fuzzy-logic.com/ch3.htm

Also, I can send you (anyone who's interested- just e-mail me at predictor@dwinnell.com) an article I published a few years ago in "PC AI" magazine, which is an introduction to applied fuzzy logic, which includes a simple image processing example.