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 [InlineMediaObject not available: see fulltext.] on a real cone K in a topological vector space E (in the sense that, for every x,y∈K, x[InlineMediaObject not available: see fulltext.]y 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 [InlineMediaObject not available: see fulltext.]. We conclude presenting a new approach to get such kind of representations, based on the concept of a biorder. Copyright Springer-Verlag 2005