MCDM'13 - paper no. 12


 

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ROBUST ORDINAL REGRESSION APPLIED TO TOPSIS

Piotr Zielniewicz

Abstract:

This paper proposes a new method for ranking a nite set of alter- natives evaluated on multiple criteria. The presented method combines the robust ordinal regression (ROR) approach and the ranking score based on the aggregate distance measure function coming from the TOPSIS method. In our method, the preference model is a set of ad- ditive value functions compatible with a non-complete set of pairwise comparisons of some reference alternatives given by the decision maker (DM). Based on this set of compatible value functions, we de ne an ag- gregate function representing relative closeness to the reference point (ideal solution) in the value space. The ranking score determined by this distance measure is then used to rank all alternatives. Calculating the distance in the value space permits to avoid normalization used in TOPSIS to transform original evaluations on di erent criteria scales into a common scale. This normalization is perceived as a weakness of TOPSIS and other methods based on a distance measure, because the ranking of alternatives depends on the normalization technique and the distance measure. Thus, ROR applied to TOPSIS does not only facilitate the preference elicitation but also solves the problem of non-meaningfulness of TOPSIS. Finally, an instructive example is given to illustrate the proposed method.

Keywords:

Multiple criteria decision aiding, robust ordinal regression, TOPSIS method, UTA^GMS and GRIP methods

Reference index:

Piotr Zielniewicz, (2013), ROBUST ORDINAL REGRESSION APPLIED TO TOPSIS, Multiple Criteria Decision Making (8), pp. 178-196

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