Existence of homogeneous representations of interval orders on a cone in a topological vector space

Necessary and sufficient conditions are presented for the existence of a pair <u,v> of positively homogeneous of degree one real functions representing an interval order on a real cone K in a topological vector space E (in the sense that, for every x,yK, xy if and only if u(x)v(y)), with u lower semicontinuous, v upper semicontinuous, and u and v utility functions for two complete preorders intimately connected with . We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder.This research has been supported by the Integrated Action of Research HI2000-0116 (Spain-Italy). Also, the work of coauthors Candeal and Induráin has been partially supported by the research project PB98-551 Estructuras ordenadas y aplicaciones (M.E.C. Spain, December 1999).