Pairwise Comparison Matrices

  • Jana KrejčíEmail author
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 366)


This chapter provides a critical review of well-known and in real-life multi-criteria decision making problems most often applied pairwise comparison methods. Three types of pairwise comparison matrices are studied in this chapter—multiplicative pairwise comparison matrices, additive pairwise comparison matrices with additive representation, and additive pairwise comparison matrices with multiplicative representation. The focus is put on the construction of pairwise comparison matrices, definitions of consistency, and methods for deriving priorities of objects from pairwise comparison matrices. Further, the transformations between the approaches for the three different pairwise comparison matrices are studied. The chapter pays a particular attention to two key properties of the pairwise comparison matrices and the related methods—reciprocity of the related pairwise comparisons and the invariance of the pairwise comparison methods under permutation of objects.


Pairwise Comparison Matrix (PCMs) Multiplicative Consistency Weak Consistency Condition Reciprocal Addition Fuzzy Preference Relations 
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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of TrentoTrentoItaly
  2. 2.Faculty of Law, Business and EconomicsUniversity of BayreuthBayreuthGermany

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