A numerical tool for multiattribute ranking problems

A large variety of techniques have been developed to solve or approximate the solution of multiattribute ranking problems. From such techniques, several implicit or explicit partial orders, defined on the same set of alternatives, are obtained (in many cases, by pairwise comparisons) with the goal of determining a linear order. Often, this goal is attained by assigning positive weights to each partial order relation. However, the imprecise judgments of the pairwise comparisons as well as other factors lead to inconsistencies which have been analyzed in an extensive literature devoted to this type of problem. In this paper, numerical results about linear extensions of weighted sum relations are applied to the recognition of pairwise imprecise judgments between alternatives as well as to the confirmation of a ranking solution as a linear extension of a quasi-order defined by a weighted sum of binary preference relations.