Operations on fuzzy sets are similar to those of standard logic but differently defined. Fuzziness and Probability Like the values considered so far, probabilities range between 0 and 1. Here too we have extremes, at one end we have deterministic systems which we can regard as having only one possible value, so the probability is always 1. These are equivalent to those scientific laws which are always true and are stable, predictable systems. At the other extreme is total freedom with infinite, stochastic, options so that the probability of any one state is effectively zero, these are unstable, indeterminate systems.
Probability is thus a measure of uncertainty, and moves towards one with increasing information.
With probability we still take the view that an option either happens or does not, so each event has a fuzzy set membership of either one or zero. Fuzziness is thus a measure of completeness and has no relation to uncertainty. We can regard this as the difference between single dimensional values and multidimensional ones The Whole in the Part Fuzzy thinking allows us to see more clearly what set membership really means. The part is its relative existence within the whole, its fuzzy set membership or completeness, Where the part equals the whole the FTV is 1 and where is no connection the FTV is 0. If we consider the whole as the available state space, then if the whole is the same as the part the probability is 1, if the whole is infinite around the part then the probability is 0.