Reduction of Pairwise Comparisons Via a Duality Approach

  • Evangelos Triantaphyllou
Part of the Applied Optimization book series (APOP, volume 44)


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).


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Evangelos Triantaphyllou
    • 1
  1. 1.Department of Industrial and Manufacturing Systems Engineering, College of EngineeringLouisiana State UniversityBaton RougeUSA

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