A general unified framework for pairwise comparison matrices in multicriterial methods | Zendy

Cavallo B. | Zendy; D'Apuzzo L. | Zendy

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A general unified framework for pairwise comparison matrices in multicriterial methods

Author(s) -

Cavallo B.,

D'Apuzzo L.

Publication year - 2009

Publication title -

international journal of intelligent systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.291

H-Index - 87

eISSN - 1098-111X

pISSN - 0884-8173

DOI - 10.1002/int.20329

Subject(s) - multiplicative function , pairwise comparison , mathematics , ranking (information retrieval) , consistency (knowledge bases) , consistency index , preference , metric (unit) , matrix (chemical analysis) , context (archaeology) , eigenvalues and eigenvectors , group decision making , abelian group , mathematical optimization , combinatorics , computer science , discrete mathematics , statistics , artificial intelligence , mathematical analysis , paleontology , materials science , operations management , physics , quantum mechanics , rheology , political science , law , economics , composite material , biology

In a multicriteria decision making context, a pairwise comparison matrix A = ( a ij ) is a helpful tool to determine the weighted ranking on a set X of alternatives or criteria. The entry a ij of the matrix can assume different meanings: a ij can be a preference ratio (multiplicative case) or a preference difference (additive case) or a ij belongs to [0, 1] and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix A has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix. © 2009 Wiley Periodicals, Inc.

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