Optimal consistent approximation of a preference matrix in decision making (Q2204267)

Summary: 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.