An algebraic/graphical tool to compare ecosystems with respect to their pollution V: cluster analysis and Hasse diagrams.

In case of large data matrices comparative evaluations of objects/regions with the technique of Hasse diagrams may be troublesome due to a messy system of lines in the graphical representation. Here fuzzy clustering leads to useful simplifications because regions with slightly different pollution pattern are grouped together. However, fuzzy clustering implies to introduce a threshold value for the membership of an object to a cluster and to select the best number of clusters. Therefore many arbitrarities evolve. Within the systematic study presented here we found that some objects are very stable against variations of the threshold value and the number of cluster whereas other objects behaves different. According to their behaviour we investigated a classification of the objects. Formal Concept Analysis shows that in some cases specific pollution pattern imply the membership to one of these classes. For example objects which are characterized by high Pb-, Zn-concentration and moderate S-concentration imply a high stability against variants of the clustering process. Further implications are described in the paper.