Conditions for the Upper Semicontinuous Representability of Preferences with Nontransitive Indifference

Abstract

We present different conditions for the existence of a pair of upper semicontinuous functions representing an interval order on a topological space without imposing any restrictive assumptions neither on the topological space nor on the representing functions. The particular case of second countable topological spaces, which is particularly interesting and frequent in economics, is carefully considered. Some final considerations concerning semiorders finish the paper.

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

“…On the other hand, it should be noted that there is a large number of contributions to the representation of nontotal binary relations (in particular nontotal preorders) in the crisp case (see e.g., Chapter 5 in Bridges amd Mehta [7], Herden and Levin [8], Herden [9], Mehta [10], Bosi et al [11], Bosi and Mehta [12], and Bosi and Zuanon [13]). This is the case when there are elements x, y ∈ X such that neither x y nor y x.…”