Solutions with fuzzy-rational generalized lotteries of III type with a one-dimensional parameter

Generalized lotteries of III type apply to cases, where both the number of alternatives and the number of consequences are countless. Since real decision makers elicit probabilities in an interval form, they disobey axioms of rationality and are called fuzzy rational decision makers. Generalized lotteries of III type, where the probability is partially described by ribbon distribution functions (constructed using interval probability measures of fuzzy rational decision makers), are called fuzzy rational generalized lotteries of III type. This paper focuses on the model of fuzzy-rational generalized lotteries of III type, defined by a one-dimensional parameter, and each containing one-dimensional prizes. The way to rank such lotteries is formalized in a three-step Q-expected utility criterion. It is implemented in a price selection problem with two Q criteria.