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Optimal consistent approximation of a preference matrix in decision making

Author

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  • Martin Gavalec
  • Hana Tomášková

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.

Suggested Citation

  • Martin Gavalec & Hana Tomášková, 2016. "Optimal consistent approximation of a preference matrix in decision making," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(4), pages 520-534.
    • Handle: RePEc:ids:ijmore:v:9:y:2016:i:4:p:520-534
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