Probabilities in the Problem of Classification - Probabilistic Composition of Preferences, Theory and Applications - page 83

Table 8.1 Representative pro les for 5 categories
Beauty Comfort Consumption Power Price Reliability Safety

c1
c11

0 0 0 0 0 0 0

c12

0 0 0 0 0 0.5 0

c13

0 0 0 0 0 0 0.5

c14

0 0 0 0 0 0.5 0.5

c2
c21

0 0 0 0 0 1 0.5

c22

0.5 0 0 0 0 0.5 0.5

c23

0.5 0 0 0 0 1 0.5

c24

0.5 0 0 0 0 1 0.5

c3
c31

0.5 0 0 0 0 1 1

c32

0.5 0.5 0 0 0 1 1

c33

1 0.5 0 0 0 1 1

c34

0.5 1 0 0 0 1 1

c4
c41

1 1 0 0.5 0 1 1

c42

1 1 0 0 0.5 1 1

c43

1 1 0 0.5 0.5 1 1

c44

1 1 0 1 0.5 1 1

c5
c51

1 1 0.5 1 0.5 1 1

c52

1 1 0.5 1 1 1 1

c53

1 1 1 1 0.5 1 1

c54

1 1 1 1 1 1 1

almost the same. Only Car11 and Car13 move, from the second and the fourth
class, respectively, to the 3rd class.
For the classi

cation combining the criteria by joint probabilities, assuming
maximal dependence, instead of a unique class as in Table 8.2 , interval classifi- -

cations appear. Table 8.3 presents three interval classi cations derived from the

probabilities of being above and below the pro les of each class calculated

employing the triangular distribution.
The

cation comparing the estimates A i + and A i − given,
respectively, by the minimum of the probabilities of being above and below by each
criterion. Then come the classi

first is the basic classi

cations resulting from application of rates of

reduction of 0.5. And, finally, those resulting from comparison of the minima by

one side to the maxima by the other.