Composition by Joint Probabilities - Probabilistic Composition of Preferences, Theory and Applications - page 40

progressive and pessimistic approach would apply. Opportunities, with a lower
priority, would receive a progressive and optimistic approach. Similarly, to costs or
weaknesses a conservative and pessimistic approach would be applied while to
risks or threats a conservative but optimistic approach might be applied.
As a general rule, to compose the groups the product will be employed and for
the rule of composition inside the groups, whenever the goal is to choose the best
alternative, the progressive and pessimistic approach is what is needed. First,
because the progressive approach focuses on the alternatives most likely to be
chosen according to each criterion separately and it is natural that these are the
alternatives more carefully measured. And the pessimistic approach leads to give
more importance to good performances according to the highest number of criteria,
while the optimistic presents a highest chance of good performances on isolated
criteria determining the outcome.
Even if the decision maker is not able to choose a point of view to decide on the
basis of joint probabilities, computing the preferences by every point of view and
comparing the results of applying such different points of view can be employed to
help identifying isolated criteria that favor certain alternatives, guiding a possible
review of the application of the criteria, in a subsequent step.

5.2 Different Assumptions About Correlation

Another aspect to consider is the modeling of the correlation between disturbances
affecting the evaluations according to different criteria.
If such correlation can be quanti

ed, it can be introduced in the computation of
the joint probabilities. However, quantifying correlations is dif cult. For instance,

in the choice of more ef cient production units, correlation between the criteria may

be expected, as the disturbances affecting the quantities of inputs used in the pro-
duction process come to affect the volumes of product. But, how does one quantify
the reciprocal influence between errors in the measurement of inputs and outputs?
The presence of correlation should be quanti

ed only in the case of positive
dependence. Negative correlation might also be considered in the case of contra-
dictory features, but the choice between satisfying opposite preference motivations
should be solved in the modeling of the criteria before entering the modeling of the
disturbances affecting them.
In the absence of a means to directly calculate the correlations, an approach that
can be taken is to compute the joint probabilities under hypotheses of independence
and of maximal dependence between all the events of the same type, i.e., between
all the events of the type ' maximizing preference according to different criteria ' ,

between all the events of the type ' not maximizing ' , between all the events of the

type .

If the difference between the scores obtained assuming independence and
assuming maximal dependence reaches signi

' minimizing ' and between all the events of the type ' not minimizing '

cant levels, research to determine the
effect of intermediary levels of dependence must be undertaken.