Reduction of Pairwise Comparisons Via a Duality Approach

Abstract

As it was discussed in previous chapters, an appealing approach for eliciting qualitative data for an MCDM problem is to use pairwise comparisons. Next suppose that a decision maker wishes to elicit the relative priorities, or weights of importance, of n entities via a sequence of pairwise comparisons. As before, these n entities could be the decision criteria, or the alternatives to be examined in terms of a single decision criterion in some MCDM problem. Then, as it was illustrated in Chapter 3, the decision maker must elicit the value of n(n−1)/2 pairwise comparisons. Therefore, if an MCDM problem involves m alternatives and n decision criteria (multiple hierarchical levels are not considered at this point), then the total number of the required pairwise comparisons is equal to n(n−1)/2 + n(m(m−1)/2).