On quasi-orderings and multi-objective functions

In the paper the relationship between quasi-orderings (i.e. transitive and reflexive relations) and multi-objective functions (i.e. functions being a finite vector of continuous value functions) is investigated. A characterization of quasi-orderings representable by multi-objective functions is given. Within the introduced theoretical framework it is, in particular, shown that preferences implied by a first order stochastic dominance relation cannot be represented by multi-objective functions.