Optimal consistent approximation of a preference matrix in decision making
by Martin Gavalec; Hana Tomášková
International Journal of Mathematics in Operational Research (IJMOR), Vol. 9, No. 4, 2016

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.

Online publication date: Sun, 16-Oct-2016

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