Hurwiczα expected utility to rank p-approximated generalized lotteries of I Type with partially quantified uncertainty

We discuss how to rank one-dimensional fuzzy-rational generalized lotteries of I type – lotteries with continuous real set of prizes, where uncertainty is partially quantifies by p-ribbon distribution functions (CDFs). The p-ribbon CDFs are interpolated on interval quantile estimates of the decision maker. We utilize the Hurwicz_α criterion under strict uncertainty to approximate the p-ribbon distribution functions into classical ones. That allows us to transform p-fuzzy rational generalized lotteries of I type into classical ones and use Hurwicz_α expected utility principle to rank those. Since the Hurwicz_α method weighs the extreme pessimism and extreme optimism, we need to first approximate the p-ribbon distribution functions using the Wald and maximax criteria under strict uncertainty (representing the extreme pessimism and extreme optimism of the fuzzy rational decision maker) before we use the Hurwicz_α criterion. A numerical example demonstrates the procedures.