3 Analytical Hierarchy Process (AHP)
19
Fig. 3.1 Hierarchy
framework
is the psychological origin of the scale used to make said comparisons, which leads
to the third pillar which is the inconsistency also denoted as the sensitivity to changes
in judgements. Prioritization is then developed giving rise to an eigenvector that can
be integrated in the AHP general feedback structure, hence reducing the mathematical method to a one-dimensional normalized ratio scale allowing a unit-less scale
measurement. This methodology can be then marked on the basis of whether or not
the ranking is preserved or reversal is allowed. Finally, implementing mathematical
methodologies into group decision making to generate individual opinions or judgements is crucial to enable the fabrication of a fundamental group decision that would
be compatible with individual predispositions.
There are several steps involved in AHP; when given a complex problem, the first
step is to construct the hierarchy framework, also known as a feedback network. This
hierarchy will have three levels: level one being the goals, level two being the different
criteria and finally, level three being the different alternative options as shown in
Fig. 3.1. The decision-making process is then initiated by systematically comparing
elements two at a time, and giving numerical weight values using scale ratios to each
element based on either actual data or subjective opinion. This is where inconsistency
can be possible, thus leading to the need to calculate the consistency index, which is a
numerical value representing variance or inconsistency. The weights are then used to
make a pairwise comparison matrix which is then used to calculate criteria weights.
The mathematical computations involved in the AHP are categorized as eigenvector
calculations where the Eigen value corresponds to each criteria weight. Depending
on the context of the problem being solved, the same could then be applied to subcriteria if they are present. In this way, we can compare criteria with differing scales,
i.e. price and size.
While the analytical hierarchy process is widely applicable to various types of
problems that vary in terms of their degrees of complexity, this method is most efficiently applied in more complicated problems that have a large number of objectives
or criteria that may include sub-divisions within them (sub-criteria). As such, for
more complex problems, it is harder to compare all the objectives to one another and
it can be significantly error prone if not approached in a systematic and consistent
manner. To resolve this problem, the AHP can be applied to complicated issues such
as the prediction of the future of higher education, design choices for a national
transport system and even recruitment options in the workplace. In addition to this,
AHP provides the decision-maker with quantified measurements of compatibility
that can then be utilized to analyse the problem manually (Lee et al. 2007).
19
Fig. 3.1 Hierarchy
framework
is the psychological origin of the scale used to make said comparisons, which leads
to the third pillar which is the inconsistency also denoted as the sensitivity to changes
in judgements. Prioritization is then developed giving rise to an eigenvector that can
be integrated in the AHP general feedback structure, hence reducing the mathematical method to a one-dimensional normalized ratio scale allowing a unit-less scale
measurement. This methodology can be then marked on the basis of whether or not
the ranking is preserved or reversal is allowed. Finally, implementing mathematical
methodologies into group decision making to generate individual opinions or judgements is crucial to enable the fabrication of a fundamental group decision that would
be compatible with individual predispositions.
There are several steps involved in AHP; when given a complex problem, the first
step is to construct the hierarchy framework, also known as a feedback network. This
hierarchy will have three levels: level one being the goals, level two being the different
criteria and finally, level three being the different alternative options as shown in
Fig. 3.1. The decision-making process is then initiated by systematically comparing
elements two at a time, and giving numerical weight values using scale ratios to each
element based on either actual data or subjective opinion. This is where inconsistency
can be possible, thus leading to the need to calculate the consistency index, which is a
numerical value representing variance or inconsistency. The weights are then used to
make a pairwise comparison matrix which is then used to calculate criteria weights.
The mathematical computations involved in the AHP are categorized as eigenvector
calculations where the Eigen value corresponds to each criteria weight. Depending
on the context of the problem being solved, the same could then be applied to subcriteria if they are present. In this way, we can compare criteria with differing scales,
i.e. price and size.
While the analytical hierarchy process is widely applicable to various types of
problems that vary in terms of their degrees of complexity, this method is most efficiently applied in more complicated problems that have a large number of objectives
or criteria that may include sub-divisions within them (sub-criteria). As such, for
more complex problems, it is harder to compare all the objectives to one another and
it can be significantly error prone if not approached in a systematic and consistent
manner. To resolve this problem, the AHP can be applied to complicated issues such
as the prediction of the future of higher education, design choices for a national
transport system and even recruitment options in the workplace. In addition to this,
AHP provides the decision-maker with quantified measurements of compatibility
that can then be utilized to analyse the problem manually (Lee et al. 2007).