In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of a semiorder, and its representability through a real-valued function and a threshold. Inspired in a recent characterization of the representability of interval orders, we obtain a full characterization of the existence of numerical representations for semiorders. This is an extension to the general case of the classical Scott-Suppes theorem concerning the representability of semiorders defined on finite sets. © 2002 Elsevier Science B.V. All rights reserved.
['Juan Carlos Candeal', 'Esteban Induráin', 'Margarita Zudaire']
Numerical representability of semiorders