There are many ranking schemes of complex entities
defined by multiple attributes. Their purpose is to determine which
decision-making unit (DMU) is “better”, which one is “worse”, or if one unit
“dominates” another. Most of those ranking endeavours require an initial
groundwork of data, which frequently introduces some subjective restrictions to
the analysis. To avoid any subjectivity, the best would be to use the “raw”
numerical values of attributes with no normalization, standardization,
aggregation, etc. In contrast with the widely used, conventional
multi-dimensional multi-criteria decision support, the authors of this paper
join those who say "let the data speak first ...". This idea is
realized in practice only by the partial order theory. It uses the
"raw" data and undeniably has the strongest mathematical basis. For
ranking purposes, a graphical representation of a partial order in the form of
a Hasse diagram is especially advantageous. It is obtained from the Hasse
matrix, embodying the relations between all the DMUs. The present paper
provides evidence that the ranking with the Data Envelopment Analysis (DEA),
which is based on a concept of efficiency does not coincide with the ranking
based on a mathematical notion of the partial order. Moreover, if all the
attributes belong to the class of outputs (“the bigger the better”) or to the
class of inputs (“the smaller the better”), the modified algorithm of the DEA with outputs only or
inputs only could be employed. If the attributes of the system belong to both
those classes, the standard DEA algorithm for DMUs with outputs only (or inputs
only) could be used after changing the values of inputs on opposite and
considering them as outputs (or changing the values of outputs on opposite and
considering them as inputs). Also, this procedure sanctions the use
of standard programs for the partial order.
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