In this paper, we go further on the problem of the continuous numerical representability of
interval orders defined on topological spaces. A new condition of compatibility between the …

We introduce the concept of quasi upper semicontinuity of a not necessarily total preorder
on a topological space and we prove that there exists a maximal element for a preorder on a …

We prove a generalization of Debreu's Open Gap Lemma. Given any subset of the real line,
this lemma guarantees the existence of a strictly increasing real function such that all the …

We analyze the main properties of binary relations, defined on a nonempty set, that arise in
a natural way when dealing with real-valued functions that satisfy certain classical functional …

We establish a partial continuous interval representation for interval orders preferences on
connected separable topological spaces. Then we provide a generalization of interval …

We introduce an upper semicontinuity condition concerning a not necessarily total preorder
on a topological space, namely strong upper semicontinuity, and in this way we extend to …

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 …

We introduce and discuss a generalization of the classical multi-objective optimization to
pairs of functions. This procedure is referred to as bi-multi-objective optimization. A …

In this thesis we first review some results concerning the real representation of preferences.
Different kind of preferences are considered and a particular attention is devoted to the case …