A Ranking Theory for Uncertain Data with Constraints

We develop a theory of top-K ranking for objects whose values may be uncertain, incomplete, or difficult to be characterized quantitatively, but between which some constraints may be required to be satisfied. We present our ranking theory for discrete space, continuous space, and the general case with probability distributions and complex constraints. The central question to be addressed is how to define the relative strengths of top-K object sequences. We show that top-K ranking defined this way in continuous space is closely related to the analysis and computation of high dimensional polyhedra, and as a consequence, the methods for the latter can be applied to compute the support ratios of top-K object sequences so that the best can be chosen.