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 sectio ns, etc.) by a multicriteria analysis is of concern, then it is often diffi cult to find a common scale among the criteria, and therefore even the simp le sorting process is performed by applying additional constraints, just to get a ranking index. However such additional constraints, often arising fr om normative considerations, are controversially discussed. The theory of p artially ordered sets and its graphical representation (Hasse diagrams) doe s 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 b attery of tests, developed by Dutka et al. In our analysis we found the fol lowing: (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 performe d within a two-dimensional grid. (2) Information, obtained from the structu re of the Hasse diagram: For example six classes of sediment sites have hig h priority, and each class exhibits a different pattern of results. (3) Los s of information, when an aggregation of test results is used in order to g uarantee complete comparability among all objects. A relation between infor mation 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 t his specific test.