Decision Making under Interval Probabilities

Authors

Ronald R. Yager
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-1999

Comments

Technical Report: UTEP-CS-98-12a

Published in International Journal of Appeoximate Reasoning, Vol. 22, No. 3, pp. 195-215.

Abstract

If we know the probabilities p(1),...,p(n) of different situations s1,...,sn, then we can choose a decision Ai for which the expected benefit C(i)=p(1)*c(i,1)+...+p(n)*c(i,n) takes the largest possible value, where c(i,j) denotes the benefit of decision Ai in situation sj. 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)] 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.