14 The Most Common Factors Effecting Ground Water Quality
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14.4 Analytical Hierarchy Process (AHP)
The analytic hierarchy process (AHP) is a structured methodology used for structuring and evaluating complicated decisions based on mathematics and psychology.
The approach was introduced by Thomas L. Saaty during the 1970s, whom collaborated with Ernest Forman to establish the Expert Choice in 1983, which has been
broadly studied and modified since. The methodology provides an accurate representation for quantifying weights of decision criterions. The process utilizes the
experiences of individual experts in order to estimate the respective magnitudes of
factors through pair-wise comparisons. Every respondent must compare the relative
importance between two factors through a specially designed survey questionnaire.
(Note that while most of the surveys adopted the five point Likert scale, AHP’s
questionnaire is 1–9 Li et al. 2019).
The analytical hierarchy process takes into account a set of evaluation criterions
and a set of alternative options, in which, between the two sets, the best decision
is selected. It should be noted, since some of the criteria may be contrasting, it is
not generally true that the best alternative is that which optimizes every individual
criterion. Rather, the alternative that attains the most suitable trade-off between the
various criteria. For each evaluation criterion, the AHP calculates a weight based on
the decision makers pair-wise comparisons for the criteria. The higher the calculated
weight is, the more important the corresponding criterion is. As for a fixed criterion, the AHP appoints a score to each alternative matching the decision maker’s
pairwise comparisons of the alternatives based on that specific criterion. The higher
the score, the better the performance of the alternatives of the corresponding criterion. Ultimately, the AHP incorporates the criteria weights and the alternative scores
resulting in a global score for every alternative as well as a consequent ranking. The
global score for a selected alternative is the weighted sum of the scores it acquired
corresponding to all the criterions.
The AHP is a very adaptable and prevailing mechanism because the scores and
final rankings are achieved based on the pair-wise comparisons of the criteria and
alternatives presented by the user. The calculations produced by the AHP are always
directed by the decision maker’s knowledge. Therefore, the AHP can be considered as
a mechanism capable of translating both qualitative and quantitative evaluations made
by the decision maker into a multi-criteria ranking. Moreover, the AHP technique
is straightforward because it does not require the structuring of a complex expert
system with the decision maker’s knowledge embedded within. Then again, the
AHP may need a large quantity of assessments by the user, particularly for problems
with various criteria and alternatives. Even though each individual assessment is
effortless, the load of the assessment task can become unreasonable given that it
only requires the decision maker to express how two alternatives or criteria compare
to each other. Furthermore, the number of pairwise comparisons quadruples with
respect to the number of criteria and alternatives. Take for example when comparing
10 alternatives on 4 criteria, 4·3/2 = 6 comparisons are required to construct the
weight vector; and 4·(10·9/2) = 180 pairwise comparisons are required to construct
133
14.4 Analytical Hierarchy Process (AHP)
The analytic hierarchy process (AHP) is a structured methodology used for structuring and evaluating complicated decisions based on mathematics and psychology.
The approach was introduced by Thomas L. Saaty during the 1970s, whom collaborated with Ernest Forman to establish the Expert Choice in 1983, which has been
broadly studied and modified since. The methodology provides an accurate representation for quantifying weights of decision criterions. The process utilizes the
experiences of individual experts in order to estimate the respective magnitudes of
factors through pair-wise comparisons. Every respondent must compare the relative
importance between two factors through a specially designed survey questionnaire.
(Note that while most of the surveys adopted the five point Likert scale, AHP’s
questionnaire is 1–9 Li et al. 2019).
The analytical hierarchy process takes into account a set of evaluation criterions
and a set of alternative options, in which, between the two sets, the best decision
is selected. It should be noted, since some of the criteria may be contrasting, it is
not generally true that the best alternative is that which optimizes every individual
criterion. Rather, the alternative that attains the most suitable trade-off between the
various criteria. For each evaluation criterion, the AHP calculates a weight based on
the decision makers pair-wise comparisons for the criteria. The higher the calculated
weight is, the more important the corresponding criterion is. As for a fixed criterion, the AHP appoints a score to each alternative matching the decision maker’s
pairwise comparisons of the alternatives based on that specific criterion. The higher
the score, the better the performance of the alternatives of the corresponding criterion. Ultimately, the AHP incorporates the criteria weights and the alternative scores
resulting in a global score for every alternative as well as a consequent ranking. The
global score for a selected alternative is the weighted sum of the scores it acquired
corresponding to all the criterions.
The AHP is a very adaptable and prevailing mechanism because the scores and
final rankings are achieved based on the pair-wise comparisons of the criteria and
alternatives presented by the user. The calculations produced by the AHP are always
directed by the decision maker’s knowledge. Therefore, the AHP can be considered as
a mechanism capable of translating both qualitative and quantitative evaluations made
by the decision maker into a multi-criteria ranking. Moreover, the AHP technique
is straightforward because it does not require the structuring of a complex expert
system with the decision maker’s knowledge embedded within. Then again, the
AHP may need a large quantity of assessments by the user, particularly for problems
with various criteria and alternatives. Even though each individual assessment is
effortless, the load of the assessment task can become unreasonable given that it
only requires the decision maker to express how two alternatives or criteria compare
to each other. Furthermore, the number of pairwise comparisons quadruples with
respect to the number of criteria and alternatives. Take for example when comparing
10 alternatives on 4 criteria, 4·3/2 = 6 comparisons are required to construct the
weight vector; and 4·(10·9/2) = 180 pairwise comparisons are required to construct