Pairwise Comparison Matrices in Decision Making

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 677)


In multicriteria decision making context, a pairwise comparison matrix is a helpful tool to determine the weighted ranking of alternatives or criteria. The entry of the matrix can assume different meanings: it can be a preference ratio (multiplicative case) or a preference difference (additive case), or, it belongs to the unit interval and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). When comparing two elements, the decision maker assigns the value from a scale to any pair of alternatives representing the element of the pairwise preference matrix. Here, we investigate particularly relations between transitivity and consistency of preference matrices being understood differently with respect to the type of preference matrix. By various methods for deriving priorities from various types of preference matrices we obtain the corresponding priority vectors for final ranking of alternatives. The obtained results are also applied to situations where some elements of the fuzzy preference matrix are missing. Finally, a unified framework for pairwise comparison matrices based on abelian linearly ordered groups is presented. Illustrative numerical examples are supplemented.


Analytic Hierarchy Process Consistency Index Pairwise Comparison Matrix Priority Vector Fuzzy Preference Relation 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of Hradec KraloveHradec KraloveCzech Republic
  2. 2.Silesian University in OpavaKarvinaCzech Republic
  3. 3.Charles University in PraguePragueCzech Republic

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