In this paper a numerical representation of preferences by means of subsets of the real line is proposed. This representation turns out to be natural for partial orderings. Some results on this representation, extending those for utility functions and pairwise representations, are provided for...

In this paper, it is shown that, under certain conditions on a preference relation defined on a set X, there exists a numerical representation by means of set-valued real functions. This kind of representation extends the usual utility function as well as the representation by means of two real...

Consider a two-person bargaining problem, where both agents have a particular notion of what would be a just solution outcome. In case their opinions differ, a procedure which leads to a compromise between t,he two different views is needed. In this paper we propose a mechanism to solve this...

On analyzing the problem that arises whenever the set of maximal elements is large, and aselection is then required (see Peris and Subiza, 1998), we realize that logical ways of selectingamong maximals violate the classical notion and axioms of rationality. We arrive at the sameconclusion if we...

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...

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...

The article proposes a new algorithm for adjusting correlation matrices and for comparison with Finger's algorithm, which is used to compute Value-at-Risk in RiskMetrics for stress test scenarios. The solution proposed by the new methodology is always better than Finger's approach in the sense...