Decision making under interval probabilities

If we know the probabilities p(1),...,p(n) of different situations s(1),... ,s(n), then we can choose a decision A(i) for which the expected benefit C- i = p(1).c(i1) + ... + p(n).c(in) takes the largest possible value, where c (ij) denotes the benefit of decision A(i) in situation s(j). In many real l ife situations, however, we do not know the exact values of the probabiliti es p(j); we only know the intervals p(j) = [p(j)(-), p(j)(+)] of possible v alues of these probabilities. In order to make decisions under such interva l probabilities, we would like to generalize the notion of expected benefit s to interval probabilities. In this paper, we show that natural requiremen ts lead to a unique (and easily computable) generalization. Thus, we have a natural way of decision making under interval probabilities. (C) 1999 Else vier Science Inc. All rights reserved.