I recently started to think about connections between Bayes' Theorem and fuzzy logic:

http://sipi.usc.edu/~kosko/Fuzziness_Vs_Probability.pdf

    (also from wikipedia on fuzzy logic):

    "Bruno de Finetti argues[citation needed] that only one 
    kind of mathematical uncertainty, probability, is 
    needed, and thus fuzzy logic is unnecessary. However, 
    Bart Kosko shows in Fuzziness vs. Probability that 
    probability theory is a subtheory of fuzzy logic, as 
    questions of degrees of belief in mutually-exclusive 
    set membership in probability theory can be represented 
    as certain cases of non-mutually-exclusive graded 
    membership in fuzzy theory. In that context, he also 
    derives Bayes' theorem from the concept of fuzzy 
    subsethood. Lotfi A. Zadeh argues that fuzzy logic is 
    different in character from probability, and is not a 
    replacement for it. He fuzzified probability to fuzzy 
    probability and also generalized it to possibility 
    theory. (cf.[10])"