Handling Conflicts in Aspectual Requirements Compositions - Transactions on Aspect-Oriented Software Development - page 153

criterion. The same process is done for the pairwise matrices corresponding to
the criteria relative importance (Table 4).
2. Next, the vectors per criterion are combined into a single matrix and this new
matrix is multiplied by the priority vector obtained from the criteria
importance matrix to obtain the overall objective (i.e., ranking of alternatives).
This process is repeated as many times as needed until the tree root is reached.
Step 5: Consistency: The logical quality of the decisions is guaranteed by
computing the consistency ratio ( CR ), which measures the consistency of the pairwise
comparison judgments:

CI

(2)

CR = p

RCI

where CI represents the consistency index and RCI is a random consistency index.
RCI is an pre-defined average random index derived from a sample of size 500 of
randomly generated reciprocal matrices [21, p. 59] and depends on the number of
elements being compared. CI is calculated using:

CI = ( max λ − n ) /( n − 1

(3)

where n is number of items being compared and λ max is obtained from:

AW = A * W

(4)

n

max ∑

λ = ( AW / W ) / n

i i

i

where A is pairwise reciprocal matrix, W weights vector, index i corresponds to each
value in the AW vector and n is again the number of elements.
If the consistency ratio CR exceeds 10%, this is indicative of inconsistent logical
judgements [20]; in such cases, the decision maker should revise the original values in
the respective pairwise comparison matrix [24]. It should be noted that this
consistency ratio ensures that the transitive property (if a>b and b>c then a>c) is
guaranteed, which means the user pairwise judgements, are logical [20].
In summary, we have chosen the AHP [20] with the simplified aggregation method
[24] because: it is a well-known and accepted method; it is appropriate for handling
conflicting concerns problems; it has the ability to quantify subjective judgements; it
is capable of comparing alternatives in relation to established criteria; it provides the
means to establish preferences (pairwise) between all criteria and between alternatives
in relation to each criterion; and it provides means to guarantee the logical
consistency of the judgements.

4 Applying AHP to the AORA Model

This section starts with a brief background on our preliminary attempts to use AHP
for conflict resolution, and then introduces an example to illustrate the proposed
application of the AHP method to the selected AORA approach [6, 7].