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D. Uzun Ozsahin et al.
the methodology followed by several simple examples that will be used to further
reinforce a more developed understanding (Saaty 2008).
1. The decision maker must define the problem and determine the kind of data they
will make the judgments on.
2. The hierarchy is structured and designed, designating the top level as the defined
goal, the second level as the broader interpretation of the determined objectives,
intermediate levels as the sub-criteria to be assessed and finally, the lowest level
will be composed of the different alternative options.
3. Using the ratio scale of relative importance developed by Saaty 1987 (Table 1.1), a
pairwise comparison matrix is constructed where all the elements are comparative
judgements made by the decision maker.
4. The pairwise matrix is normalized, and the criteria weights are derived as the
average of each row in the matrix.
5. Using the derived criteria weights, we can find the Eigen vector (ω) by calculating
the weight sum value for each criterion.
6. The Eigen value (λ) is then found such that Aω = λω
7. Finally, the consistency index is calculated to legitimize the reliability of the
decision maker’s judgments.
3.3 Theoretical Apprehension of Consistency
The concept of consistency is one of the essential step of the analytical hierarchy
process. In principle, the consistency ratio is calculated as the reliability of the preferential judgments in comparison to a large number of randomly generated judgments.
Realistically, inconsistency is inevitable as it is non-avoidable, primarily because
the foundation of decision making is based on the personal preference of the decision maker and it is inevitable that inconsistency will occur in the preference of the
decision maker. In other words, the input of the AHP system is based on personal
preference and therefore highly prone to human error (Dyer and Forman 1991). The
question at hand is the degree of the consistency and whether or not it satisfies the
predetermined standard values (Mu and Pereyra-Rojas 2017).
To quantify the level of consistency in the problem at hand, the consistency ratio
is derived as the ratio of the consistency index to the random index. The consistency
index represents the consistency of the pairwise matrix of the given problem. On the
other hand, the random index matrix is a representation of the average consistency
ratio of 500 randomly generated pairwise matrices. These values are predetermined
and constant; they are singularly dependent on the dimensions (n) of the problem at
hand. The calculated values are illustrated in Table 3.2. Based on the previous work
of Saaty regarding the complexities of the concept of consistency in the analytical
hierarchy process, the consistency ratio is defined as CR where CR = CI/RI (Saaty
2012). He also eluded that the standard CR value is 0.1, meaning that if the consistency ratio is calculated to be equivalent to or less than the standard 0.1 value, then the
problem is acceptably denoted as consistent and the analysis process is legitimized.
D. Uzun Ozsahin et al.
the methodology followed by several simple examples that will be used to further
reinforce a more developed understanding (Saaty 2008).
1. The decision maker must define the problem and determine the kind of data they
will make the judgments on.
2. The hierarchy is structured and designed, designating the top level as the defined
goal, the second level as the broader interpretation of the determined objectives,
intermediate levels as the sub-criteria to be assessed and finally, the lowest level
will be composed of the different alternative options.
3. Using the ratio scale of relative importance developed by Saaty 1987 (Table 1.1), a
pairwise comparison matrix is constructed where all the elements are comparative
judgements made by the decision maker.
4. The pairwise matrix is normalized, and the criteria weights are derived as the
average of each row in the matrix.
5. Using the derived criteria weights, we can find the Eigen vector (ω) by calculating
the weight sum value for each criterion.
6. The Eigen value (λ) is then found such that Aω = λω
7. Finally, the consistency index is calculated to legitimize the reliability of the
decision maker’s judgments.
3.3 Theoretical Apprehension of Consistency
The concept of consistency is one of the essential step of the analytical hierarchy
process. In principle, the consistency ratio is calculated as the reliability of the preferential judgments in comparison to a large number of randomly generated judgments.
Realistically, inconsistency is inevitable as it is non-avoidable, primarily because
the foundation of decision making is based on the personal preference of the decision maker and it is inevitable that inconsistency will occur in the preference of the
decision maker. In other words, the input of the AHP system is based on personal
preference and therefore highly prone to human error (Dyer and Forman 1991). The
question at hand is the degree of the consistency and whether or not it satisfies the
predetermined standard values (Mu and Pereyra-Rojas 2017).
To quantify the level of consistency in the problem at hand, the consistency ratio
is derived as the ratio of the consistency index to the random index. The consistency
index represents the consistency of the pairwise matrix of the given problem. On the
other hand, the random index matrix is a representation of the average consistency
ratio of 500 randomly generated pairwise matrices. These values are predetermined
and constant; they are singularly dependent on the dimensions (n) of the problem at
hand. The calculated values are illustrated in Table 3.2. Based on the previous work
of Saaty regarding the complexities of the concept of consistency in the analytical
hierarchy process, the consistency ratio is defined as CR where CR = CI/RI (Saaty
2012). He also eluded that the standard CR value is 0.1, meaning that if the consistency ratio is calculated to be equivalent to or less than the standard 0.1 value, then the
problem is acceptably denoted as consistent and the analysis process is legitimized.