Approaches to Criteria Combination - Probabilistic Composition of Preferences, Theory and Applications - page 11

Table 2.4 Cars evaluations
Beauty Comfort Consumption Power Price Reliability Safety

Car1

1 1 1 0 1 1 0

Car2

1 1 1 0 1 0 1

Car3

1 1 1 0 0 1 1

Car4

1 1 0 1 0 1 1

Car5

1 1 0 1 0 1 0

Car6

1 1 0 1 0 0 1

Car7

1 1 0 0 1 1 1

Car8

1 1 0 0 1 1 0

Car9

1 1 0 0 0 1 1

Car10

1 0 1 1 0 1 1

Car11

1 0 1 0 1 0 1

Car12

1 0 0 1 1 1 1

Car13

1 0 0 1 0 1 1

Car14

1 0 0 0 1 1 1

Car15

0 1 1 1 1 1 0

Car16

0 1 1 1 0 1 1

Car17

0 1 1 0 1 1 1

Car18

0 1 0 1 0 1 1

Car19

0 0 1 1 0 1 1

Car20

0 0 0 1 1 1 1

Comparing the weighted averages generated multiplying the value 0 or 1
assigned to the model according to each criterion by the weight of the criterion and
adding the products, Car 17, with a score of 0.94, would be chosen.

2.3 Capacities

The classical approach to the composition of multiple criteria, described in the
preceding section, employs weighted averages of the evaluations according to the
multiple criteria. This form of composition is justi

ed if the decision can be thought

of as a two-stage structure: first, one of the criteria is chosen, with the chance of

being chosen depending on the importance that the decision maker wants to give it;
then, the chosen criterion is applied alone. In that case, the probability of an
alternative being chosen is determined by the Total Probability Theorem, provided
in the Appendix, as the weighted average of its probabilities of being chosen