This note provides two numerical representations of a nested system of strict partial orders. The first representation is based on utility and threshold functions. We generalize the threshold representation of menu-dependent preferences by allowing the threshold to depend not only on the menu...

This note provides two numerical representations of a nested system of strict partial orders. The first representation is based on utility and threshold functions. We generalize the threshold representation of menu-dependent preferences by allowing the threshold to depend not only on the menu...

We characterize weak continuity of an interval order on a topological space by using the concept of a scale in a topological space.

Numerical representations of choice functions allow the expression of a problem of choice as a problem of finding maxima of real valued functions, which requires less information to be defined and which is easier to work with. In this paper, the existence of numerical representations of choice...

In this paper we analyze the existence of three different kinds of continuous numerical representations for binary relations by using a finite measure defined on the space of alternatives. Each one of these kinds of representation is suitable for a different class of binary relations. Thus we...