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groups. Reliability and safety form a group of two criteria of high priority and the
other
five criteria are considered of lower priority.
The criteria of high priority are combined by a progressive and pessimistic point
of view and those of lower of priority are combined by a progressive and optimistic
point of view. The two groups are
finally combined pessimistically, so that the
final
score is given by the probability of being preferred by the two groups.
Thus, the
five criteria of low priority are combined in terms of probability of
being the best by at least one of them and, assuming independence, the
final score is
obtained multiplying this joint probability by the product of the probabilities of
preference by the two other criteria.
Beside the joint probability scores, is presented in Table 5.1 a column with the
vector of scores standardized to sum 1 and a column with the ranks. For com-
parison, in a last column are repeated the ranks obtained by weighted average with
the weights of Table 2.3 .
It can be seen in Table 5.1 that the ranking obtained by joint probabilities is
similar to that obtained by weighted average with higher weights for the criteria
receiving now high priority, with the
final choice of cars 17 and 16. The concor-
dance between the results of application of these two approaches is con
rmed by a
ranks correlation coef
cient of 0.88.
The joint probabilities in Table 5.1 are calculated assuming independence. The
results of analogous computation assuming the hypothesis of maximal dependen-
cies are presented in Table 5.2 . It can be noticed how the hypothesis of maximal
dependence considerably reduces the variation. In fact, only four different values
are observed for the
final scores there.
In this example of car models, as the evaluations by each criterion present only
two possible values, minimizing is equivalent to not maximizing. The next example
has a larger set of possible values.
In this second example are compared the performances of drivers of a fleet of
urban buses. The drivers are grouped by the shifts of the bus line they work for.
Four criteria are employed to assess individual performance: based on two process
attributes and on two output attributes.
The process attributes are related to the speed kept in various parts of the route to
avoid large spacing between two buses of the same line, which would increase the
chance of passengers taking buses of competing companies. To build these process
attributes, the times each vehicle passes by previously determined points are
recorded. These attributes, denoted T 1 and T 2 , are, respectively, the number of
passages at each of these points before a predetermined small time threshold and
after another higher one.
The output attributes, denoted by P 1 and P 2 , are the number of passengers
transported by the driver and by the whole shift of the driver.
Table 5.3 shows the weekly improvement in each of these attributes referring to
ten drivers of the three shifts of a bus line. The attributes are measured in terms of
weekly variation, what means, for instance, that a positive value of 3 in T 1 signi
es
that the driver presented this week less 3 transgressions of the passage thresholds
relatively to the previous week.
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