Showing papers by "Hans De Meyer published in 2012"
Journal Article•
TL;DR: In this article, the authors present some developments in the field of partial order theory which prove to be helpful in applications where a ranking is needed, and quantify how close the result of each tool is to a ranking of the pesticides, a linearity index is introduced.
Abstract: Ranking chemicals according to their potential environmental hazard is a well accepted preparatory step in risk assessment. A study of Halfon et al. ranked pesticides by applying simple tools on the partially ordered set (poset) induced by chemical properties as proxies for their groundwater contamination hazard. In this contribution, we present some developments in the field of partial order theory which prove to be helpful in applications where a ranking is needed. Whereas in the former study a classification of the pesticides in only four classes was obtained, in the current contribution tools are used that aim at a greater differentiation to support decision makers and to allow for comparison with monitoring results. In order to quantify how close the result of each tool is to a ranking of the pesticides, a linearity index is introduced.
14 citations
09 Jul 2012
TL;DR: The class of variolinear copulas covers the subclasses of semilinear, ortholinear and biconic copulas, whose construction has been reported before and focuses on the situation where the variability of the line segments is governed by two linear functions.
Abstract: We construct variolinear copulas with a given diagonal section, i.e. copulas that are linear on line segments connecting points on the diagonal to points on the boundary of the unit square. These line segments cover the unit square, two line segments can only intersect at (0,1) or (1,0), and the line segments may have a varying angle w.r.t. the main diagonal. The class of variolinear copulas covers the subclasses of semilinear, ortholinear and biconic copulas, whose construction has been reported before. We restrict the analysis to the case of symmetric variolinear copulas and we focus on the situation where the variability of the line segments is governed by two linear functions. For that subclass we provide the necessary and sufficient conditions on a diagonal function to obtain a variolinear copula. Some examples are provided.
2 citations
09 Jul 2012
TL;DR: This paper focuses on stochastic transitive opening of reciprocal relations, presenting theoretical results as well as a practical method to construct such transitive openings.
Abstract: For crisp as well as fuzzy relations, the results concerning transitive closures and openings are well known. For reciprocal relations transitivity is often defined in terms of stochastic transitivity. This paper focuses on stochastic transitive openings of reciprocal relations, presenting theoretical results as well as a practical method to construct such transitive openings.
2 citations
09 Jul 2012
TL;DR: This contribution reveals a remarkable relationship between the 3-cycle condition and the number of so-called product triplets of a reciprocal relation and experimentally counts product doublets for several families of winning probability relations.
Abstract: It is known that the winning probability relation of a dice model, which amounts to the pairwise comparison of a set of independent random variables that are uniformly distributed on finite integer multisets, is dice transitive. The condition of dice transitivity, also called the 3-cycle condition, is, however, not sufficient for an arbitrary rational-valued reciprocal relation to be the winning probability relation of a dice model. An additional necessary condition, called the 4-cycle condition, is introduced in this contribution. Moreover, we reveal a remarkable relationship between the 3-cycle condition and the number of so-called product triplets of a reciprocal relation. Finally, we experimentally count product triplets for several families of winning probability relations.