Incomparable: what now II? Absorption of incomparabilities by a cluster method

When newer compilations of decision support methods are examined, partial order methods as a central methodological aspect are rarely found. This is strange, since the role of multi-indicator systems is worldwide increasing. Multi-indicator systems induce in a natural manner partial orders. Why is partial order not seen as that important tool? The main reason appears to be that partially ordered sets are in general not completely ordered. There are incomparabilities, and incomparabilities do not lead to rankings. Thus, incomparabilities a priori hamper any decision. Approaching the decision from the need to get a unique ranking, it is clear that decision support systems aim toward deriving a one-dimensional scalar, by which a linear, i.e. a unique order can be derived. In the present paper an approach is selected to reduce the number of incomparabilities without losing the quality of insights, partially ordered sets allow. As an example economical relevant chemicals are studied.