The transferable belief model and random sets

1) Quantified beliefs are point-valued, not interval-valued 2) Any connection with randomization or necessary additivity as encountered within probability theory has been explicitly eliminated. 3) A difference has been established between open and closed world assumptions (Smets 1988). The normalization after conditioning and combination is not performed in the open world context. 4) A two-level model for the beliefs has been proposed (Smets 1989a). It consists of a credal level where beliefs are entertained and a pignistic level where beliefs are used to make decisions. At the credal level, beliefs are quantified by belief functions. At the pignistic level, beliefs are quantified by probability functions. When a decision must be made, the beliefs at the credal level are transformed into beliefs at the pignistic level, i.e. there exists a transformation from the belief functions to the probability functions. It is called the pignistic transformation (Smets 1989b). It corresponds to the Generalized Insufficient Reason Principle. 5) The justification of the TBM is based on the idea that the impact of an evidence consists in allocating parts m(A) of an initial unitary amount of belief among the propositions A of a given algebra. m(A) is that part of our belief that supports A and that, due to lack of information, does not support any strict subproposition of A. The m are called the basic belief masses (bbm). 6) The definition of bel (and pl) are derived from the bbm, and the inequalities among the belief functions are deduced.