Multicriteria prioritization and partial order in environmental sciences

Abstract

The complexity of the present data-centric world finds its expression in the increasing number of multi-indicator systems. This has led to the development of multicriteria ranking systems based on partial orders. Order theory is a main pillar of structural mathematics. Partial orders help to reveal why an object of interest holds a certain ranking position and how much it is subject to change if a composite indicator is upgraded. Order theory helps to derive linear or weak orders without indicator weighting schemes. Hence, rankings obtained from decision support systems (DSS) which depend on many parameters beyond the data matrix can be checked and discrepancies can lead to examine the parameters of the DSS. Order theory helps discover association and implication structures derived from formal concept lattices. Association and implication networks among the attributes of the data matrix allow more insights into multi-indicator systems and lead to new hypotheses and motivate further research. Some new and innovative concepts, like separated subsets, antagonistic indicators, ranking stability fields are rendered. Separated subsets are the typical outcome of a partial order analysis; their identification leads to antagonistic indicators, which are responsible for the separatedness of object’s subsets. Numerical aggregation can be performed step-by-step and the question which values of a weight lead to an order inversion is of high interest. The concept of stability fields is one possible answer, discussed in this paper. After an outline of partial order theory some more specific theoretical results are shown, then we discuss the role of composite indicators in the light of partial order and give some examples of interesting applications of partial order. Finally examples are selected from real life case studies of watersheds, environmental performance evaluations, child well being, geographic and administrative regions and more.