No intelligent decision support system functions even remotely without knowing the preferences of the user. A major problem is that the way average users think about and formulate their preferences does not match the utility-based quantitative frameworks currently used in decision support systems. For the average user qualitative models are a better fit. This paper presents an argumentationbase...

Abstract This paper presents a solution to a superoptimal version of the block AAK problem Given a rational and antistable matrix function R s R s R s and a nonnegative integer k nd all superoptimal approximations Q s with no more than k poles in the right half complex plane that minimise the supremum over the imaginary axis of the singular values of the error function E s R s R s Q s with resp...

Ptolemaic graphs are graphs that satisfy the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs, and it is a natural generalization of block graphs (and hence trees). In this paper, a new characterization of ptolemaic graphs is presented. It is a laminar structure of cliques, and leads us to a canonical tr...

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over {0, . . . , q− 1} as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defin...

Then, define u(xyz) = 100 ∗ U(x) + 10 ∗ U(y) + U(z), where x ∈ {red, blue, green}, y ∈ {electric, petrol, diesel}, and z ∈ {German, French,UK}. Observe that for all x, x′ ∈ {red, blue, green}with x 6= x′, and y, y′ ∈ {electric, petrol, diesel} with y 6= y′, and z ∈ {German, French,UK} we have that (i) |U(y)− U(y′)| > U(z), and (ii) |U(x)− U(x′)| > U(y) + U(z). Intuitively, this ensures that the...

We describe some ideas and results about the following problem: Given a set, a family of \preference relations" on the set, and a \priority" among those preference relations, which elements of the set are best? That is, which elements are most preferred by a consensus of the preference relations which takes account of their relative priority? The problem is posed in a deliberately general way, ...

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCPnets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The pape...

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another extension concerns bipolar fuzzy sets, where ...

This paper presents and evaluates uncoordinated on-line algorithms for simultaneous storage and replication load-balancing in DHTbased peer-to-peer systems. We compare our approach with the classical balls into bins model, and point out both the similarities as well as the differences which call for new load-balancing mechanisms specifically targeted at P2P systems. Some of the peculiarities of...