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...

We analyze the structure of a semiorder, paying attention to its representability through a real-valued function and a positive constant threshold (the so-called Scott-Suppes representation). We furnish a new set of sufficient conditions for the Scott-Suppes representability of semiorders....