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 life situations, however, we do not know the exact values of the probabilities p(j); we only know the intervals p(j) = [p(j)(-), p(j)(+)] of possible values of these probabilities. In order to make decisions under such interval probabilities, we would like to generalize the notion of expected benefits to interval probabilities. In this paper, we show that natural requirements lead to a unique (and easily computable) generalization. Thus, we have a natural way of decision making under interval probabilities. (C) 1999 Elsevier Science Inc. All rights reserved.