Ranking fuzzy sets and fuzzy random variables by means of stochastic orders

Abstract

This paper establishes a theory of decision making under uncertainty with fuzzy utilities. The extension of expected utility and stochastic dominance to the comparison of sets of random variables plays a crucial role. Their properties as fuzzy rankings are studied, and their definitions are further generalized to the comparison of fuzzy random variables. Also, a connection between expected utility for fuzzy random variables and the comparison of the lower/upper probabilities they induce is proven