Abstract: A generalized family of partial orders is studied, which is semiparametrized by a utility function f and a distortion function g , namely, (f,g) -utility and distorted stochastic dominance ( (f,g) -UDSD). Such a family is especially suitable for representing a decision maker’s preferences in terms of risk aversion. We characterize the monotonicity of the partial order in the rank-dependent utility model, and the isotonic classes of rank-dependent utility with (f,g) -UDSD are also established. Inspired by the concept of the congruent utility class, we introduce the definition of the congruent distortion class. The characterization of the congruent utility class or distortion class of (f,g) -utility and distorted stochastic dominance is investigated. Based on the main results in this paper, we unify some related results in the existing literature. As an application, we propose a general approach to develop a continuum between first-order stochastic dominance and second-order stochastic dominance based on the partial order.