An approach to combine cluster analysis with order theoretical tools in problems of environmental pollution
To uniformly deal with data of environmental pollution, we represent objects (in this case regions) of an ecological examination as elements of a partially ordered set. The results are visualized by Hasse diagrams. To reduce the complexity of our posets, methods of cluster analysis are used. There is also a question of statistical significance of the ordinal relations. In particular we present an algorithm that first calculates an unsharp partition (using a method of fuzzy clustering) of an object set. Next the unsharp partition is transformed to a sharp one with the aim to define a new order. By splitting the quality function it can be shown that objects which cannot be assigned to clusters forming ensembles of more than one element contribute to the method's error. A strategy minimizing that error is proposed.
cluster analysis environmental pollution hasse diagrams posets fuzzy chemicals evaluation