Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019 5.3
CALCULATING THE PRIORITY VALUES OF BINARY COMPARISON MATRICES
The pairwise comparison matrices obtained in the third step have priority values. In this context, the pairwise comparison matrices are subjected to normalization process. For this, first of all each value in the matrix is divided by the total number of columns. Thus, the values in the matrix (0, 1) are converted to the values in the open range and the sum of each column is 1.
This new matrix obtained is the normalized matrix. By taking the arithmetic average of each row in this matrix, the priority values of the elements compared can be reached.
5.4 CALCULATION OF CONSISTENCY RATIO
In the fourth step, the consistency of comparisons is examined. The binary comparison matrices consist of the personal judgment of the decision-maker. Furthermore, the best way to cope with complexity is consistency and this can be demonstrated by the best analytical approach (Korsakiene, 2004).
For this, the Consistency Ratio (CR) values are calculated. When CR > 0.10, it is understood that there is no consistency and that comparisons should be reviewed. The value of CR is calculated with the help of equation (1):
CR = CI / RI (1)
The value in the denominator of the formula is the Random Index (RI) value. RI takes values varying according to matrix size (n) and these values are given as ready tables. RI values for different n values are shown in Table 4.
Table 4. RI values for different units (Labib, 2011). N 2
3 10 4 11 5 12 6 13 7 14 8 15 RI 1.45 1.49 1.51 1.54 1.56 1.57 1.59
RI 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 N 9
9 -
-
The expression CI in the equation (1) is known as the Consistency Index (CI). CI is calculated by equation (2) below:
CI = (max - n) /(n - 1) (2)
n in the formula shows the size of the matrix and λmax shows the maximum eigenvector.
5.5
CALCULATION OF FINAL PRIORITY VALUES
In the last step of the method, the final priority values are calculated. In this step, a number of expression processes are carried out, resulting in the final weights for the
alternatives. As a result, it is recommended to select the alternative with the highest weight.
5.6 APPLICATION OF AHP
Five criteria developed in relation to strengths were compared in pairs. The evaluations made by three experts whose evaluations were consistent among eight experts (CR2: 0,121; CR7: 0,125; CR8: 0,129), were taken into consideration (The value of CRi; i = 1, 2, ..., 8, indicates the consistency ratio of the ith decision maker.). As a result of the evaluations of consistent decision-makers, the weights of each criterion were obtained by taking arithmetic averages and the final weights were determined. These are respectively (0,307), (0,081), (0,278), (0,139) and (0,194). Then, the criteria is reduced to 3 by selecting criteria 1, 3 and 5, which have the highest weight values. These criteria are determined as the strongest criterions as S1, S3 and S5 in the rest of the analysis.
Five criteria developed in relation to weaknesses were compared in pairs. The evaluations made by three experts whose evaluations were consistent among eight experts (CR1: 0,08; CR3: 0,07 and CR6: 0,08) were taken into consideration. As a result of the evaluations of consistent decision-makers, the weights of each criterion were obtained by taking arithmetic averages and the final weights were determined. These are respectively (0,317), (0,102), (0,186), (0,152) and (0,240). The number of criteria is reduced to 3 by selecting criteria 1, 3 and 5, which have the highest weight values. These criteria are determined as the strongest criterions as W1, W3 and W5 in the rest of the analysis.
Five criteria developed in relation to opportunities were compared in pairs. The evaluations made by three experts whose evaluations were consistent among eight experts (CR1: 0,069; CR3: 0,072 and CR6: 0,063) were taken into consideration. As a result of the evaluations of consistent decision-makers, the weights of each criterion were obtained by taking arithmetic averages and the final weights were determined. These are respectively (0,334), (0,096), (0,157), (0,196) and (0,215). The number of criteria is reduced to 3 by selecting criteria 1, 3 and 5, which have the highest weight values. These criteria are determined as the strongest criterions as O1, O4 and O5 in the rest of the analysis.
Five criteria developed in relation to threats were compared in pairs as well as others. The evaluations made by three experts whose evaluations were consistent among eight experts (CR1: 0,072; CR5: 0,054 and CR7: 0,055), were taken into consideration. As a result of the evaluations of consistent decision-makers, the weights of each criterion were obtained by taking arithmetic averages and the final weights were determined. These are respectively (0,239), (0,073), (0,158), (0,391) and (0,137). The number of criteria is reduced to 3 by selecting criteria 1, 3 and 4, which have the highest weight values. These
©2019: The Royal Institution of Naval Architects
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