Multiple Criteria Decision Analysis - Probabilistic Composition of Preferences, Theory and Applications - page 3

dif culty of detection of the modes of failure to generate one-dimensional risk

priority probabilities.
In this context, the probabilistic approach has the advantage of allowing for

flexible rules for aggregating risks generated by different factors. To increase dis-
crimination between modes of failure related to those factors for which the scores
are concentrated in a small interval, the probabilistic distributions may be modeled
with a range varying with the observed range. However, to give the evaluators the
option of spacing the scores only to discriminate according to factors that they
judge more relevant, the probabilistic approach allows for modeling the distribution
of the evaluations according to the three factors with the same range, determined by
extremes previously established.
Another field of application is the assessment of productivity. The probabilistic

approach can be applied in the context of evaluating the ef

ciency of production
units employing compositions of sets of inputs to generate sets of outputs. In the
probabilistic approach to this problem, the criteria can be the output/input ratios for
the different pairs of input-output.
The decision may also be based on maximizing each output variable and min-
imizing each input variable separately. Then, a criterion will be associated with
each input and each output. In this last form of modeling, the probabilities of
preference according to each criterion to be computed will be, respectively, those
of maximizing the revenue from the sale of each product and of minimizing the cost
of the acquisition of each resource. Different treatments can then be applied to the
aggregation of the two separate sets of evaluations, according to inputs and
according to outputs.
The uniformization provided by the probabilistic transformation may be used to
extend the possibility of application of capacities. In fact, to combine evaluations
according to different criteria by the integral of Choquet with respect to a capacity
in the set of criteria, the evaluations enter the computation ordered according to the
values taken. This does not make sense unless the evaluations are set in a same
framework. The transformation into probabilities of being the best provides this
common framework.
The transformation into probabilities of being the best also has an effect of
approximating to identical values the preferences for the alternatives less preferred.
This feature makes the probabilistic approach useful in other contexts. For instance,
it can be used to provide rough measurements to the decision attributes in appli-
cations of Rough Sets Theory with Dominance There, it allows for reducing con-
tradictions and extracting simpler decision rules.