Multiple Criteria Decision Analysis - Probabilistic Composition of Preferences, Theory and Applications - page 2

Another case of decision problems is that of sorting, which consists of selecting
from among some predetermined classes the most suitable to place an alternative.
This can be seen as a choice problem in which what is chosen is, for each alter-
native, the most suitable from among a small number of classes. In this sorting
problem, a preference between the alternatives is established whenever the prede-
termined classes, where such alternatives are classi ed, are previously ranked.

ed by a small set of representative alternatives. In
the case of multi-criteria analysis, the vector of the evaluations of each of the class
representative alternatives using the multiple criteria forms what is called a class
reference pro

Each class is previously identi

le.

1.3 Probabilities of Choice

In a probabilistic framework, attention is given to subjective aspects of the decision
problem that make it impossible to evaluate the alternatives precisely. In the fol-
lowing chapters, an approach to take into account the presence of uncertainty in the
assessments of preference and thereby to generate rules for ranking or sorting the
alternatives based on probabilities of choice is presented for each decision problem.
The fact that the main interest of the decision maker — and often the sole interest —
is to choose the best alternative offers a path to simplify the probabilistic modeling of
the problem. In such an approach, the vectors of values of the attributes of interest
give way to vectors of probabilities for presenting the best value for these attributes.
Even if a ranking of all the options is desired, a better idea of the possibilities of
ranks

' inversion can be provided if the final ranking is derived from probabilities of

being the best alternative.
Additionally, the importance of the different criteria for the choice becomes
clearer if the corresponding evaluations are given in terms of probabilities of being
the best according to each of them. Moreover, with all the evaluations given in the
same terms, the problem of combining evaluations generated by employing dif-
ferent measurement standards is eliminated.
The next two chapters prepare the presentation of this probabilistic approach.
After being fully developed in Chaps. 4 - 8 , it is applied in the three last chapters in

speci c contexts.

1.4 Applications of the Probabilistic Approach

This probabilistic approach is applied, for instance, to the evaluation of risks,
helping to detect the risks that are of higher priority. In this case, the application
consists of combining risk ratings according to different sources of risk. The
probabilistic composition can be applied to combine the scores of risk according to
the factors of Failure Modes and Effects Analysis (FMEA): severity, frequency, and