Catálogo de publicaciones - libros

The corner stone in the development of decision support systems is to secure that the partial ordering of descriptors does reflect reality. The similarity between descriptor ranking and field scale data ranking is thus highly critical and this chapter shows how to establish this linkage. The partial order technique is used as a robust and non-parametric similarity quantification method and illustrated using monitoring data of pesticide findings in streams of Denmark. The approach has a general appeal where the consequence of false positives (accidentally identification of a similarity) is critical and/or only rough knowledge exist about relations between the data sets that are going to be analysed for similarity. A simple and transparent mapping of a correlation profile is possible and the software named Po Correlation supports the principle described in this chapter. The principle is an extension of the conventional that is modified to include ordering using more than two data sets simultaneously and thus being a kind of a multi-variate rank correlation analysis. The multi-variate nature opens up for several measures of discordance that shows different aspects of discrepancy between the data set. A graphical display using Hasse diagrams of respectively concordant and discordant rankings shows how individual objects are respectively correlated and anti-correlated with regard to all the other objects. A testing algorithm using randomized data sets are included in order to test for statistically significance of both similarity and discrepancy.

The construction of posets or Hasse diagrams is a profitable means for the evaluation of biomonitoring data. In contrast to other statistical approaches the Hasse Diagram Technique enables the consideration of multiple attributes at the same time and will result in at least partially ordered data sets. Moreover, the calculation of averaged ranks allows the construction of a total order for a given data set. For the evaluation of biomonitoring data, as obtained for the German Environmental Specimen Bank, the Hasse diagram technique was applied to achieve partially or totally ordered data. The following scheme was applied: i) Careful rounding of the original data to increase the number of comparabilities; ii) splitting of the data in smaller sub-sets; iii) construction of the posets for each sub-set; iv) construction of the total order for each sub-set (by means of averaged ranks) and, v) synopsis of the sub-sets.

Potential habitat suitability was assessed for species groupings of vertebrate fauna in the State of Pennsylvania, USA as part of a nationally coordinated GAP Analysis Program to find gaps in provision for conservation of important habitats. Diversity values were compiled spatially at a resolution of one square kilometre from species models developed at 30-meter resolution. Diversity patterns differ in varying degrees among species groups for mammals, birds, amphibians, snakes/lizards, turtles, and fishes. Comparing the patterns for partial ordering on watershed extents using statistical indices of ranking can facilitate determination of inter-group commonality and contrast. This helps to designate watersheds as having importance from multi-group and particular group perspectives. Partial ordering on the basis of rank-range runs is particularly informative when combined with levels of counter-indication corresponding to levels in a Hasse diagram. This serves to segregate sets having combinatorial clarity of condition relative to conservation from settings where disparate conditions may offer opportunities for targeted restoration. Disparity of conditions on multiple bio-indicators may arise from habitat heterogeneity as well as differential degradation. Broadening the spectrum of indicators will usually increase the apparent complexity of the conservation context.

The main objective of the European Commission’s White Paper on a future chemicals strategy (EEC 2001) is to facilitate the risk assessment of chemicals leading to, where necessary, risk reduction. Important roles play the chemical and environmental databases, which can be regarded as an information turnover. In this paper the emphasis lies on the evaluation of 12 numerical databases available on the free Internet, which focus on environmental fate and ecotoxicity as well as on high production volume chemicals. Hence we analyse a 12×27 data-matrix in the first place. Two multi-criteria evaluation and decision support instruments are applied: The Hasse Diagram Technique (HDT), a method derived from discrete mathematics, and the Method of Evaluation by Order Theory (METEOR). The original data-matrix of 12 databases (objects) and 27 parameters (attributes) will be subject to several logical aggregation steps. The aim of the aggregation procedure that can be performed by applying iteratively the Hasse Diagram Technique (HDT) is to get a unique prioritisation scheme. Significant data gaps even on the chosen well-known high production volume chemicals as well as on ecotoxicity and environmental fate parameters are identified by the chosen methods and weighting procedures. This indicates an alarming signal concerning the new existing chemicals policy of the EEC.

We give a brief introduction to the notion of concept, a mathematical model of conceptual thinking. It serves very well in the organization of interviews, tests and evaluations, since it allows a systematic way of drawing conclusions and establishing hypotheses. Thus, it can be considered as an efficient tool for decision support, for example, in environmental risk management. In fact, it models a certain way of doing research by gathering examples and trying pattern recognition.

A partial order of longstanding interest to mathematicians and chemists, the Young Diagram Lattice (YDL) is discussed in the context of complexity. Ruch’s (1975) identification of this partially ordered set with that appropriate to a general partial ordering for mixing is discussed. A mathematical quantity associated with each member of the set (the cardinality of maximal anti-chains for that member) is argued to provide a quantitative measure for complexity for members of the set. The measure has the desirable feature that low complexity is associated with both highly ordered and very random systems, while systems that have intermediate “structure” have larger complexity. Several quantitative examples based on the YDL are briefly discussed including statistical mechanics, diffusion, and biopolymeric complexity. Finally, a metaphor for complexity suggested by the YDL associates high complexity with posetic incomparability. Examples from sociology, ecology, and politics are discussed.

This chapter describes the evolution of the use of Hasse diagrams in the environmental field and the development of the related software. Two Italian scientists, Marcello Reggiani and Roberto Marchetti, used Hasse diagrams to study the problem of model order estimation. Halfon extended the use of Hasse diagrams to ecological modelling and later to environmental chemistry. The HASSE software was initially developed in FORTRAN to be run on mainframe computers. Later Halfon in Canada and Brüggemann in Germany reprogrammed it for use on personal computers and code was added to display the diagrams interactively. Nowadays, scientific groups in Denmark, Germany, Italy and Sweden are actively developing new applications and developing new theoretical concepts.

We give a brief introduction to the notion of concept, a mathematical model of conceptual thinking. It serves very well in the organization of interviews, tests and evaluations, since it allows a systematic way of drawing conclusions and establishing hypotheses. Thus, it can be considered as an efficient tool for decision support, for example, in environmental risk management. In fact, it models a certain way of doing research by gathering examples and trying pattern recognition.