Continuous representability of interval orders

Abstract

In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order, and its representability through a pair of continuous real-valued functions. Inspired in recent characterizations of the representability of interval orders, we obtain new results concerning the existence of continuous real-valued representations. Classical results are also restated in a unified framework.

Keywords

• Orderings on a set
• Interval orders
• Numerical representations of orderings
• Continuous representations of orderings