Pairwise support maximization methods to exploit valued outranking relations in ranking problems

Many outranking methods involve two steps. First, the alternatives are compared pairwise to build a valued outranking relation; this relation is then exploited to derive a recommendation for the decision maker. We present three related exploitation models providing three types of solutions, depending on the decision maker’s request: a linear order, a weak order, or a weak partial order. Each solution is evaluated by computing the support for the pairwise comparisons it implies. This comparison may be based on the minimum support present in the solution (prudence principle), the lexicographically minimum support, or the sum of the supports. Relations between these models and some of their properties are discussed and illustrated using data sets found in the literature.