Ranking discrete outcome alternatives with partially quantified uncertainty

Abstract

Real decision makers (DM) partially quantify uncertainty as probability uncertainty intervals. Then alternatives are modeled as fuzzy-rational lotteries. Those can be approximated by standard lotteries with point-estimate probabilities, referred as classical-risky. Ranking the approximating classical-risky lotteries is a problem under risk, solved by expected utility. However, the approximation itself is a problem under strict uncertainty. Here this part of the problem is solved by criteria under strict uncertainty, which if not perfectly rational, are well worked descriptive methods with known properties. The proposed Laplace, Wald, maximax and Hurwiczα expected utility criteria for prescriptive ranking of fuzzy-rational lotteries allow the DM to control the approximation of alternatives with partially quantified uncertainty in consistency with her/his degree of belief and with his optimism–pessimism attitude. That makes them superior to the widespread abandoned-m and normalized mean criteria, which often violate the intrinsic subjective probabilities of the DM. The proposed criteria are generalizations of expected utility criterion under risk and of their standard versions under strict uncertainty.