Pairwise Comparisons Based Non-Numerical Ranking

A systematic procedure for deriving weakly ordered non-numerical rankings from given sets of data is proposed and analysed. The data are assumed to be collected using the Pairwise Comparisons paradigm. The concept of a partially ordered approximation of an arbitrary binary relation is formally defined and some solutions are proposed. The problem of testing and the importance of indifference and the power of weak order extensions are also discussed.