Real representations of preferences and applications.

In this thesis we first review some results concerning the real representation of preferences. Different kind of preferences are considered and a particular attention is devoted to the case of intransitivity of the associated indifference relation. Therefore, interval orders and semiorders appear as relevant types of binary relations for which indifference is not transitive. It is particulary interesting to guarantee the existence of continuous or at least upper semicontinuous representations. Homogeneity of the representations is studied in connection with the aforementioned continuity when the space of preferences is endowed with an algebraic structure.