A basic problem in multi-criteria decision-making (MCDM) is to find a ranking for alternatives
which are not directly comparable with each other. A number of different methods exists. In …

We give an overview of some new trends in preference modeling, utility representation, and
choice rationalization. Several recent contributions on these topics point in the same …

The study of complexity and optimization in decision theory involves both partial and
complete characterizations of preferences over decision spaces in terms of real-valued …

We introduce a new class of real-valued monotones in preordered spaces, injective
monotones. We show that the class of preorders for which they exist lies in between the …

On the basis of the classical continuous multi-utility representation theorem of Levin on
locally compact and σ-compact Hausdorff spaces, we present necessary and sufficient …

Although there is a somewhat standard formalization of computability on countable sets
given by Turing machines, the same cannot be said about uncountable sets. Among the …

The present paper gives a topological solution to representability problems related to multi-
utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of …

Consumers' preferences and choices are traditionally described by appealing to two
classical tenets of rationality: transitivity and completeness. In 1971, Schmeidler proved a …

The study of intelligent systems explains behaviour in terms of economic rationality. This
results in an optimization principle involving a function or utility, which states that the system …

The well-known notion of dimension for partial orders by Dushnik and Miller allows to
quantify the degree of incomparability and, thus, is regarded as a measure of complexity for …