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Table 7.1 Scale of preference between two parameters
Scale
Degree of
preference
Explanation
1
Equally
Two activities contribute equally to the objective
3
Moderately
Experience and judgement slightly to moderately favour
one activity over another
5
Strongly
Experience and judgement strongly or essentially favour
one activity over another
7
Very strongly
An activity is strongly favoured over another and its
dominance is showed in practice
9
Extremely
The evidence of favouring one activity over another is
of the highest degree possible of an af rmation
2, 4, 6 and 8
Intermediate
values
Used to represent compromises between the references
in weight 1, 3, 5, 7 and 9
Reciprocals
Opposites
Used for inverse comparison
numerical value was accomplished with the help of comparative oral judgment and
synthesis of priorities. A couple comparing matrix was constructed on the basis of
the preference of a factor as compared with the other factor and arithmetic mean
method was applied to arrange landslide triggering factors hierarchically and to
determine prioritized factor rating value/eigenvector (PFRV) with reasonable
consistency ratio (CR) on MATLAB software after Saaty ( 1980 ) (Table 7.2 ). To
develop pair-wise comparison matrix, each factor/class was rated against every
other factor by assigning a relative dominant value ranging between 1 and 9 on the
basis of the relative importance of the factors in terms of landslide frequency. The
value also varies between the reciprocals 1/2 and 1/9 for inverse comparison
(Table 7.1 ).
Another appealing feature of the AHP is the ability to evaluate pair-wise rating
inconsistency. The eigenvalues enable to quantify a consistency measure which is
an indicator of the inconsistencies or intransivities in a set of pair-wise ratings.
Saaty presented that for a consistent reciprocal matrix, the largest eigenvalue
ʻ Max is
equal to the number of comparisons n (Table 7.2 ).
In AHP, an index of consistency, known as the CR (Consistency Ratio), is used
to indicate the probability that the matrix judgements were randomly generated
(Saaty 1994 ).
CR
¼
CI
=
RI
ð 7 : 2 Þ
where RI is the average of the resulting consistency index depending on the order of
the matrix given by Saaty and CI is the consistency index that is expressed in the
following equation. If the value of CR is smaller or equal to 10 %, the inconsistency
is acceptable, but if the CR is greater than 10 %, the subjective valued judgement
needs to be revised.
A measure of consistency, called consistency index CI, is de
ned as follows:
 
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