Composition by Joint Probabilities - Probabilistic Composition of Preferences, Theory and Applications - page 46

first exploratory analysis of this data set highlights the best weekly evolution
of the performance of the drivers of Shift 2, regarding both the

A

final output and the

process attributes.
Tables 5.4 and 5.5 show the result of the transformation into probabilities of
reaching the upper and lower ranks in each attribute, assuming triangular distri-
butions with extremes given by the lowest and highest values observed in Table 5.3 ,
that means, 4 and 5 for P 1 and 3 and 9 for P 2 .

Very similar results are obtained if larger ranges are assumed for these distributions.
In Table 5.5 , the high values

3 and 0 for T 1 , 4 and 0 for T 2 ,

− − −

for the probabilities of driver D 21
minimizing T 1 , driver D 33 minimizing T 2 and driver D 31 minimizing P 1 deserve
attention. This is an illustration of the ability of the probabilistic transformation
to detach the extreme alternatives by considering the two frontiers, of best and
worst performances. Looking only at Table 5.4 the values of the maximization

— above 0.3 —

Table 5.4 Probabilities of being the best
T 1 T 2 P 1 P 2

D 11

0.1532 0.0373 0.2606 0.0140

D 21

0.0092 0.0574 0.0632 0.0140

D 31

0.1532 0.1159 0.0200 0.0140

D 12

0.1532 0.1159 0.1594 0.2045

D 22

0.1532 0.1159 0.0955 0.2045

D 32

0.1532 0.1159 0.0632 0.2045

D 13

0.0289 0.2763 0.1594 0.0861

D 23

0.0289 0.0277 0.0955 0.0861

D 33

0.0140 0.0220 0.0465 0.0861

D 43

0.1532 0.1159 0.0367 0.0861

Table 5.5 Probabilities of being the worst
T 1 T 2 P 1 P 2

D 11 0.0472 0.1013 0.0449 0.2691

D 21 0.4146 0.0648 0.0693 0.2691

D 31 0.0472 0.0475 0.4038 0.2691

D 12 0.0472 0.0475 0.0508 0.0246

D 22 0.0472 0.0475 0.0586 0.0246

D 32 0.0472 0.0475 0.0693 0.0246

D 13 0.0731 0.0376 0.0508 0.0298

D 23 0.0731 0.1922 0.0586 0.0298

D 33 0.1563 0.3664 0.0848 0.0298

D 43 0.0472 0.0475 0.1090 0.0298