Showing papers by "Hans De Meyer published in 2009"
TL;DR: A method to relabel noisy multi-criteria data sets is presented, taking advantage of the transitivity of the non-monotonicity relation to formulate the problem as an efficiently solvable maximum independent set problem.
38 citations
TL;DR: The best-possible upper bound for the set of copulas with a given opposite diagonal section being known is focused on, which in general is a quasi-copula which exhibits an interesting type of bivariate symmetry called opposite symmetry.
Abstract: In this paper, we study opposite diagonal sections of quasi-copulas and copulas. The best-possible upper bound for the set of copulas with a given opposite diagonal section being known, we focus on the best-possible lower bound, which in general is a quasi-copula. Moreover, it exhibits an interesting type of bivariate symmetry called opposite symmetry.
30 citations
Journal Article•
TL;DR: This work focuses particular attention on the family of orbital semilinear copulas, which are obtained by linear interpolation on segments connecting the diagonal and opposite diagonal of the unit square.
Abstract: We introduce four families of semilinear copulas (i. e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital semilinear copulas, which are obtained by linear interpolation on segments connecting the diagonal and opposite diagonal of the unit square.
21 citations
TL;DR: Assuming differentiability of these additive generators, equivalent sufficient conditions that can be expressed as inequalities involving derivatives of the additive generators are proposed, avoiding the need of composing them.
Abstract: Dominance between triangular norms (t-norms) is a versatile relationship. For continuous Archimedean t-norms, dominance can be verified by checking one of many sufficient conditions derived from a generalization of the Mulholland inequality. These conditions pertain to various convexity properties of compositions of additive generators and their inverses. In this paper, assuming differentiability of these additive generators, we propose equivalent sufficient conditions that can be expressed as inequalities involving derivatives of the additive generators, avoiding the need of composing them. We demonstrate the powerfulness of the results by the straightforward rediscovery of dominance relationships in the Schweizer-Sklar t-norm family, as well as by unveiling some formerly unknown dominance relationships in the Sugeno-Weber t-norm family. Finally, we illustrate that the results can also be applied to members of different parametric families of t-norm.
14 citations
TL;DR: It turns out that the characterization of the optimal strategies is completely different for each game variant of the (n, sigma)(P) games.
Abstract: We introduce three variants of a symmetric matrix game corresponding to three ways of comparing two partitions of a fixed integer (sigma) into a fixed number (n) of parts, In the random variable interpretation of the game, each variant depends on the choice of a copula that binds the marginal uniform cumulative distribution functions (cdf) into the bivariate cdf. The three copulas considered are the product copula T-P and the two extreme copulas, i.e. the minimum Copula T-M and the Lukasiewicz copula T-L. The associated games are denoted as the (n, sigma)(P), (n, sigma)(M)and (n, sigma)(L) games. In the present paper, we characterize the optimal strategies of the (n, sigma)(M) and (n, sigma)(L) games and compare them to the optimal strategies of the (n, sigma)(P) games. It turns out that the characterization of the optimal strategies is completely different for each game variant.
3 citations