On reducing inconsistency of pairwise comparison matrices below an acceptance threshold

Sándor Bozóki (), János Fülöp () and Attila Poesz ()

Central European Journal of Operations Research, 2015, vol. 23, issue 4, 849-866

Abstract: A recent work of the authors on the analysis of pairwise comparison matrices that can be made consistent by the modification of a few elements is continued and extended. Inconsistency indices are defined for indicating the overall quality of a pairwise comparison matrix. It is expected that serious contradictions in the matrix imply high inconsistency and vice versa. However, in the 35-year history of the applications of pairwise comparison matrices, only one of the indices, namely $${ CR}$$ C R proposed by Saaty, has been associated to a general level of acceptance, by the well known ten percent rule. In the paper, we consider a wide class of inconsistency indices, including $${ CR}$$ C R , $${ CM}$$ C M proposed by Koczkodaj and $${ CI}$$ C I by Peláez and Lamata. Assume that a threshold of acceptable inconsistency is given (for $${ CR}$$ C R it can be 0.1). The aim is to find the minimal number of matrix elements, the appropriate modification of which makes the matrix acceptable. On the other hand, given the maximal number of modifiable matrix elements, the aim is to find the minimal level of inconsistency that can be achieved. In both cases the solution is derived from a nonlinear mixed-integer optimization problem. Results are applicable in decision support systems that allow real time interaction with the decision maker in order to review pairwise comparison matrices. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Multi-attribute decision making; Pairwise comparison matrix; Inconsistency; Mixed 0–1 convex programming (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s10100-014-0346-7

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