Abstract
An axiomatic derivation of the U-uncertainty that is simpler than the standard proof which covers the case of sub-normal possibility distributions is presented. The standard deviation uses an extremely complex branching axiom which is equivalent to the branching axiom presented. While the terminology used is possibility theory, a fuzzy set can be considered as an unordered and sub-normal possibility distribution. As a consequence the correct measure of uncertainty for a fuzzy set is U(A) = ∫0h(A) log2|αA|+(1-h(A))log2|s(A)|.