Paper Info
Title
On reducing inconsistency of pairwise comparison matrices below an acceptance threshold
Abstract
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 \({ CR}\) 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 \({ CR}\), \({ CM}\) proposed by Koczkodaj and \({ CI}\) by Peláez and Lamata. Assume that a threshold of acceptable inconsistency is given (for \({ CR}\) 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.
Year
DOI
Venue
2015
10.1007/s10100-014-0346-7
Central European Journal of Operations Research
Keywords
Field
DocType
Multi-attribute decision making,Pairwise comparison matrix,Inconsistency,Mixed 0–1 convex programming
Pairwise comparison,Mathematical optimization,Nonlinear system,Matrix (mathematics),Optimization problem,Decision maker,Pairwise comparison matrix,Mathematics
Journal
Volume
Issue
ISSN
23
4
1613-9178
Citations 
PageRank 
References 
6
0.43
10
Authors
3
Name
Order
Citations
PageRank
Sándor Bozóki115810.98
J. FüLöP21007.91
Attila Poesz3281.75