Approaches to Criteria Combination - Probabilistic Composition of Preferences, Theory and Applications - page 10

If the value of the Consistency Ratio is smaller or equal to 10 %, the incon-
sistency is acceptable. If the Consistency Ratio is greater than 10 %, the subjective
judgment must be revised.

2.2.3 Example of AHP Application

This subsection deals with the problem of choice of a car model. Suppose the space
of alternatives formed of 20 models and six criteria based on a satisfactory answer
for the presence or absence of seven attributes: beauty, comfort, gas consumption,
power, acquisition price, reliability and safety.
Table 2.2 presents the ratios a given decision maker consider to more adequately
reflect the preference between the seven criteria corresponding to the presence or
absence of each of the seven attributes.
The highest eigenvalue for this positive reciprocal matrix is 7.335. So, its

consistency index is (7.335 1) = 0.056. The consistency ratio is 0.056/

1.32 = 0.042 < 0.1. So, the inconsistency is acceptable and a unitary eigenvector
corresponding to this eigenvalue will be used as the vector of weights. Given by
this unitary eigenvector, the weights are those in Table 2.3 .
Table 2.4 describes the evaluation of 20 models according to the seven criteria
directly based on these attributes.

− 7)/(7 −

Table 2.2 Criteria pairwise evaluation
Beauty Comfort Consumption Power Price Reliability Safety

Beauty 1/3 1/5 1/3 1/9 1/9

1 1

Comfort 1/3 1/5 1/5

3 1 3 3

Consumption 1/3 1/3

5 3 1 3 5

Power 1/3 1/3 1/3 1/9 1/9

1 1

Price 1/3 1/5 1/7 1/7

3 3 1

Reliability

9 5 3 9 7 1 1

Safety

9 5 3 9 7 1 1

Table 2.3 Criteria weights
Beauty Comfort Consumption Power Price Reliability Safety

0.03

0.08 0.15 0.03 0.05 0.33 0.33