4 research outputs found
On the geometric mean method for incomplete pairwise comparisons
When creating the ranking based on the pairwise comparisons very often, we
face difficulties in completing all the results of direct comparisons. In this
case, the solution is to use the ranking method based on the incomplete PC
matrix. The article presents the extension of the well known geometric mean
method for incomplete PC matrices. The description of the methods is
accompanied by theoretical considerations showing the existence of the solution
and the optimality of the proposed approach.Comment: 15 page
Incomplete analytic hierarchy process with minimum weighted ordinal violations
Incomplete pairwise comparison matrices offer a natural way of expressing
preferences in decision making processes. Although ordinal information is
crucial, there is a bias in the literature: cardinal models dominate. Ordinal
models usually yield non-unique solutions; therefore, an approach blending
ordinal and cardinal information is needed. In this work, we consider two
cascading problems: first, we compute ordinal preferences, maximizing an index
that combines ordinal and cardinal information; then, we obtain a cardinal
ranking by enforcing ordinal constraints. Notably, we provide a sufficient
condition (that is likely to be satisfied in practical cases) for the first
problem to admit a unique solution and we develop a provably polynomial-time
algorithm to compute it. The effectiveness of the proposed method is analyzed
and compared with respect to other approaches and criteria at the state of the
art.Comment: preprint submitted to the International Journal of General System