3
Imprecise Probabilities for Treating Uncertainty
As described in Chapter 1, it has been argued that in situations of poor knowledge, representations of uncertainty based on lower and upper probabilities are more appropriate than precise probabilities. This chapter presents imprecise probabilityes for treating uncertainty, largely taken from Aven (2011c).
The first theoretical foundation for imprecise probability was laid down by Boole (1854). More recently, Peter M. Williams developed a mathematical foundation for imprecise probabilities based on de Finetti's betting interpretation of probability (de Finetti, 1974). This foundation was further developed independently by Kuznetsov (1991) and Walley (1991).
The term “imprecise probability” brings together a variety of different theories (Coolen, Troffaes, and Augustin, 2010). It is used to refer to a generalization of probability theory based on the representation of the uncertainty about an event A through the use of a lower probability 
and an upper probability 
, where 
. The imprecision in the representation of event 
is defined as ...
