Applying the concept of partially ordered sets on the ranking of near-shore sediments by a battery of tests.

When a ranking of some objects (chemicals, geographical sites, river sections, etc.) by a multicriteria analysis is of concern, then it is often difficult to find a common scale among the criteria, and therefore even the simple sorting process is performed by applying additional constraints, just to get a ranking index. However such additional constraints, often arising from normative considerations, are controversially discussed. The theory of partially ordered sets and its graphical representation (Hasse diagrams) does not need such additional information just to sort the objects. Here, the approach of using partially ordered sets is described by applying it to a battery of tests, developed by Dutka et al. In our analysis we found the following: (1) The dimension analysis of partially ordered sets suggests that, at least in the case of the 55 analyzed samples and the evaluation by the scores, developed by Dutka et al., there is a considerable redundancy with respect to ranking. The visualization of the sediment sites can be performed within a two-dimensional grid. (2) Information, obtained from the structure of the Hasse diagram: For example six classes of sediment sites have high priority, and each class exhibits a different pattern of results. (3) Loss of information, when an aggregation of test results is used in order to guarantee complete comparability among all objects. A relation between information drawn from the graphic and the uncertainty of ranking after using an aggregation is given. (4) The sensitivity analysis identifies one test as most important, namely the test for Fecal Coliforms/Escherichia coli. This means that the ranking of samples is heavily influenced by the results of this specific test.