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In-Depth Information
Figure 23.1
Hierarchical structure of decision-making.
compare the importance from c11 to c32, it is necessary to know their global priority values.
Their global priority values are their local priority values multiplied by the weight of their
superior criterion.
Let's assume that the local priority values for c11, c12 and c13 are 0.2, 0.2 and 0.4, which
means within criterion 1, c11 is equally important to c12 and half as important as c13. The global
priority values for c11, c12 and c13 are their local values multiplied by the weight of c1 (0.4),
which are 0.08, 0.08 and 0.16. Actually the local priority value of each sub-criterion is their
preference weight within one criterion while the global priority value is their preference weight
that can be used to make a comparison across the whole level.
At last, after having the global priority values for each sub-criterion, the decision maker needs
to pair-wise compare all the alternatives regarding their real performance on each sub-criterion
and provide a quality score for each sub-criterion of each alternative. For example, there are
alternatives A, B and C. As for the performance regarding sub-criterion 1, Alternative A is
equally as good as B but twice as good as C, then the quality scores of this sub-criterion for each
alternative are 0.4, 0.4 and 0.2 (the calculation process is the same as the calculation for
the priority values). So the total preference for each alternative is given by global priority
value ∗ quality score of each sub-criterion. Eventually, the ranking of the alternatives and fi nal
decision can be made based on these preference values.
In addition, this method uses subjective judgments from respondents. And in order to make
sure the judgments of the respondents are consistent with each other through the whole
process, the AHP allows a consistency ratio measurement, which is used to check whether the
comparisons of respondents are rational in terms of consistency. For example, if one respondent
thinks A is twice as important as B and B is equally important as C, then when he compares
A and C, he should think A is about twice important than C. However, the method does not
require the respondents to be perfectly consistent during the whole paired comparisons.
The rule of thumb is that the consistency ratio should be equal to or less than 0.1 to make sure
this respondent is rational and consistent enough. Otherwise, the evaluation of this respondent
cannot be used as a valid data.
Unlike asking respondents to assign preference values to each sub-criterion directly, this
method helps respondents to go through the whole decision-making process step by step, from
the comparison between broad criteria to the comparison between the sub-criteria within each
broad criteria. This hierarchical process of pair-wise comparison enables respondents to make the
judgements easier and more accurate. And this advantage makes the AHP a good method to deal
