The influence on partial order ranking from input parameter uncertainty: Definition of a robustness parameter

The method of partial order ranking has been used within the environmental area for a variety of purposes as an attractive way of handling complex information. However, the environmental data are often associated with a significant degree of uncertainty. In this investigation the general nature of the influence from data uncertainty on the partial order ranking is analyzed. A Monte Carlo type analysis is performed in which a series of randomly formed data are used to test the influence of data uncertainty. The partial order ranking is interpreted, where the results are transferred to a one-dimensional ranking scale taking into account that not all elements are ranked with the same certainty. A simple general robustness parameter (E) in form of the expected number of comparisons for each ranking element is defined and correlated to the uncertainty analysis results. A simple equation relates E to the number of elements and the number of parameters, respectively. The magnitude of the ranking uncertainty is shown to increase rapidly when the E value decreases below 4–5 comparisons per element. When the E value exceeds 5 the ranking uncertainty becomes nearly constant and independent on the actual E value.