Annals of Operations Research

, Volume 274, Issue 1–2, pp 155–169 | Cite as

A general formulation for some inconsistency indices of pairwise comparisons

  • Matteo BrunelliEmail author
  • Michele Fedrizzi
Original Research


We propose a unifying approach to the problem of measuring the inconsistency of judgments. More precisely, we define a general framework to allow several well-known inconsistency indices to be expressed as special cases of this new formulation. We consider inconsistency indices as aggregations of ‘local’, i.e. triple-based, inconsistencies. We show that few reasonable assumptions guarantee a set of good properties for the obtained general inconsistency index. Under this representation, we prove a property of Pareto efficiency and show that OWA functions and t-conorms are suitable aggregation functions of local inconsistencies. We argue that the flexibility of this proposal allows tuning of the index. For example, by using different types of OWA functions, the analyst can obtain the desired balance between an averaging behavior and a ‘largest inconsistency-focused’ behavior.


Pairwise comparisons Multiplicative preference relations Consistency Inconsistency index Analytic hierarchy process Aggregation OWA functions 



The authors acknowledge the anonymous reviewers for their constructive comments which helped improve the original version of this manuscript.


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Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of TrentoTrentoItaly

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