Weights of Road Accident Causes using Analytic Hierarchy Process
Weights of Road Accident Causes using Analytic Hierarchy Process
Weights of Road Accident Causes using Analytic Hierarchy Process
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VOL. 2, NO. 2, March 2012 ISSN 2225-7217<br />
ARPN Journal <strong>of</strong> Science and Technology<br />
©2011-2012. All rights reserved.<br />
http://www.ejournal<strong>of</strong>science.org<br />
Table-4.1. Criteria Pair-wise comparison AHP.<br />
Cn C1 C2 C3 C4<br />
C1 1 3 1/3 1/7<br />
C2 1/3 1 1/7 1/9<br />
C3 3 7 1 1/3<br />
C4 7 9 3 1<br />
Step 3: Find Eigenvector and Eigen-value <strong>of</strong> the criterion.<br />
Eigenvector and eigenvalue are obtained <strong>using</strong> equation (1) and (2).<br />
For example the calculation <strong>of</strong> weights criteria is:<br />
Eigenvector, A ij =<br />
( 1×<br />
3×<br />
1/<br />
3×<br />
1/<br />
7)<br />
Table-4.2. Eigenvector and Eigen-value <strong>of</strong> criterion.<br />
Cn C1 C2 C3 C4 ( ) n 1/<br />
1 × ...× c A n<br />
ij<br />
i<br />
C1 1 3 1/3 1/7 3/5 0.0989 4.0596<br />
C2 1/3 1 1/7 1/9 1/4 0.0434 4.1489<br />
C3 3 7 1 1/3 1 5/8 0.2616 4.0534<br />
C4 7 9 3 1 3 5/7 0.5962 4.1314<br />
Total 6 2/9 1 16.3943<br />
1/<br />
4<br />
=<br />
0.<br />
09889<br />
2<br />
6<br />
9<br />
The eigenvector <strong>of</strong> each criterion is computed as the<br />
example given.<br />
To obtain the consistency ratio (CR), the calculation <strong>of</strong><br />
Eigen-value is needed as follows:<br />
λ<br />
Eigen value, i<br />
( 1×<br />
0.<br />
098856 + 3×<br />
0.<br />
043368 + 1/<br />
3×<br />
0.<br />
261556 + 1/<br />
7 × 0.<br />
596217)<br />
=<br />
0.<br />
098859<br />
= 4.<br />
05956<br />
Next, calculate the consistency index (CI) <strong>using</strong> equation<br />
(3).<br />
⎛16.<br />
3948 ⎞<br />
⎜ − 4⎟<br />
Consistency test, CI = ⎝ 4 ⎠<br />
= 0.<br />
03285<br />
3<br />
The calculation <strong>of</strong> Consistency Ratio (CR) is 0.0365 by<br />
equation (4). Thus, the judgment is acceptable since CR is<br />
less than 0.1.<br />
Step 4 : Compute the eigenvector and Eigen-value <strong>of</strong><br />
alternatives pair-wise measurement and CR. The<br />
alternatives Table are illustrated as Table-4.3<br />
The calculations <strong>of</strong> the eigenvector, Eigen-value and<br />
consistency ratio are computed as same as example and<br />
formula from above.<br />
c<br />
λ<br />
Table-4.3. Alternatives pair-wise comparison with<br />
respect to criteria <strong>of</strong> Car, C1.<br />
C1 A1 A2 A3 A4 A5<br />
A1 1 5 7 3 3<br />
A2 1/5 1 1/5 1/5 1/3<br />
A3 1/7 5 1 1/3 3<br />
A4 1/3 5 3 1 1<br />
A5 1/3 3 1/3 1 1<br />
Table-4.4. Eigenvector and Eigen-value <strong>of</strong> alternatives<br />
with respect to criteria, C1.<br />
1 / n<br />
C1 ( )<br />
× An<br />
ij A i<br />
A1<br />
... ×<br />
A1 3 1/6 0.4800 5.6268<br />
A2 1/3 0.0464 5.4579<br />
A3 1 0.1420 6.1851<br />
A4 1 3/8 0.2096 5.4856<br />
A5 4/5 0.1219 5.5612<br />
Column<br />
sum<br />
6 4/7 1 28.3168<br />
The CR <strong>of</strong> the matrix above is 0.1480. Thus, the judgment<br />
is acceptable since CR is less than 0.1.<br />
In addition, the weights priorities for the hierarchy <strong>of</strong><br />
alternatives with respect to each criterion are also<br />
computed as the same way. Table-4.5 is shown from the<br />
result <strong>of</strong> weights calculation for each alternative to the<br />
criterion.<br />
Step 5 : Compute the composite priority (Overall<br />
weights in the entire hierarchy).<br />
λ<br />
42
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