Title: Optimal consistent approximation of a preference matrix in decision making

Authors: Martin Gavalec; Hana Tomášková

Addresses: Faculty of Informatics and Management, University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové, Czech Republic ' Faculty of Informatics and Management, University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové, Czech Republic

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.

DOI: 10.1504/IJMOR.2016.079810

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.4, pp.520 - 534

Received: 15 Dec 2014
Accepted: 08 May 2015

Published online: 23 Sep 2016 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article