Optimal consistent approximation of a preference matrix in decision making

Martin Gavalec and Hana Tomášková

International Journal of Mathematics in Operational Research, 2016, vol. 9, issue 4, 520-534

Abstract: A new approach to the inconsistency problem of preference matrices is described. The optimal consistent approximation (OCA) is computed as a consistent matrix with the minimal distance from the given (not necessarily consistent) preference matrix A. The approximation is found by a linear optimisation method under the assumption that A is antisymmetric. Moreover, a modified method (MOCA) is suggested for treating incomplete preference matrices. MOCA can also be used for identifying so-called outliers, i.e., the entries badly influencing the distance of the nearest consistent approximation. Outliers are usually caused by errors in data processing. The methods are illustrated by examples.

Keywords: decision making; incomplete preference matrices; consistent preference matrix; optimisation; optimal consistent approximation; OCA; outliers. (search for similar items in EconPapers)
Date: 2016
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