Min-transitivity of graded comparisons for random variables

Classically, the comparison of random variables have been done by means of a crisp order, which is known as stochastic dominance. In the last years, the classical stochastic dominance have been extended to a graded version by means of a probabilistic relation. In this work we propose different ways of measuring the gradual order among random variables by using fuzzy relations instead of probabilistic relations. The connection between the cycle-transitivity of the probabilistic relation and the T-transitivity of the associated fuzzy weak preference relation is characterized in the particular case of the minimum t-norm.