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Applying Data Envelopment Analysis Principle in Ordinal Multi Criteria Decision Analysis

Kress Moshe

Foundations of Computing and Decision Sciences

2021

Vol. 46, No. 2

147--157

We consider a multicriteria decision analysis (MCDA) problem where importance of criteria, and evaluations of alternatives with respect to the criteria, are expressed on a qualitative ordinal scale. Using the extreme-point principle of Data Envelopment Analysis (DEA), we develop a two-parameter method for obtaining overall ratings of the alternatives when preferences and evaluations are made on an ordinal scale. We assume no parametric setup other than the two parameters that reflect minimum intensities of discriminating among rank positions: one parameter for the alternatives’ ranking and one for the criteria ranking. These parameters are bounded by the ordinal input data, and they imply a universal tie among the alternatives when both parameters are selected to be zero. We describe the model, discuss its theoretical underpinning, and demonstrate its application.

Rankings as ordinal scale measurement results

Muravyov S. V.

Metrology and Measurement Systems

2007

Vol. 14, nr 1

9-23

Rankings (or preference relations, or weak orders) are sometimes considered to be non-empirical, non-objective, low-informative and, in principle, are not worthy to be titled measurements. A purpose of the paper is to demonstrate that the measurement result on the ordinal scale should be an entire (consensus) ranking of n objects ranked by m properties (or experts, or voters) in order of preference and the ranking is one of points of the weak orders space. The consensus relation that would give an integrative characterization of the initial rankings is one of strict (linear) order relations, which, in some sense, is nearest to every of the initial rankings. A recursive branch and bound measurement procedure for finding the consensus relation is described. An approach to consensus relation uncertainty assessment is discussed.