Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P( A) is used, typically satisfying Kolmogorov’s axioms. Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and consistency of information, and thus it is often too restrictive to cope carefully with the multi-dimensional nature of uncertainty. Perhaps the most straightforward restriction is that the quality of underlying knowledge cannot be adequately represented using a single probability measure. An increasingly popular and successful generalization is available through the use of lower and upper probabilities, denoted by \( \underline {P}(A)\) and \(\overline {P}(A)\) respectively, with \(0\leq \underline {P}(A) \leq \overline {P}(A) \leq 1\) , or, more generally, by lower and upper expectations (previsions). The special case with \( \underline {P}(A)=\overline {P}(A)\) for all events A provides precise probability, whilst \( \underline {P}(A)=0\) and \(\overline {P}(A)=1\) represents complete lack of knowledge about A, with a flexible continuum in between. Some approaches, summarized under the name nonadditive probabilities, directly use one of these set-functions, assuming the other one to be naturally defined such that \( \underline {P}(A^c)= 1-\overline {P}(A)\) , with A c the complement of A. Other related concepts understand the corresponding intervals \([ \underline {P}(A), \overline {P}(A)]\) for all events as the basic entity. Informally, \( \underline {P}(A)\) can be interpreted as reflecting the evidence certainly in favour of event A, and \(1-\overline {P}(A)\) as reflecting the evidence against A hence in favour of A c .