ABSTRACT
Dempster (1968) suggested a method of inference using upper and lower probabilities, which was extended and named belief functions by Shafer (1976). These models provide many simple expressions of familiar concepts from statistics, logic and natural language (see Almond, 1991). They are based on complementary set functions BEL (A) and PL (A), the belief and plausibility, respectively, which provide lower and upper bounds on the probability that the outcome will lie in the set A. When BEL (A) = PL(A), then the belief function behaves like an ordinary probability distribution and is said to be Bayesian. Corresponding to the upper and lower probabilities, upper and lower expectations, E̱(U) and Ē(U), can be defined for an unknown variable U.
