25
3.2.5.1. Criteria Weighting
A scale from 1= equally important through 9= extremely important was used to record the relative level of importance for the pairwise combinations of
the decision elements. It had confirmed that a scale of nine units was reasonable and reflected the degree which could discriminate the intensity of relationships
between elements. Each member of the group first orders the decision elements to be compared so the statement “element A is preferred over element B”was
correct, and then recorded the appropriate rating value 1 to 9 for the strength of the opinion.
Tabel 1. Importance Level
RATING IMPORTANCE LEVEL
1 Equally important
2 Equally to moderately more important
3 Moderately more
important 4
Moderately to strongly more important 5 Strongly
more important
6 Strongly to very strongly more important
7 Very strongly more important
8 Very strongly to extremely more important
9 Extremely more important
The number of judgments needed for a particular matrix of order n, the number of element being compared, was nn-12 because it is reciprocal and the
diagonal elements are equal to unity. An element of pairwise comparison matrix a
ij
represented a relative importance of element I compared with element j. A consistent pairwise comparison held the following conditions:
ij ij
a a
1 =
≠∝ ≥
ij ij
a a
;
ij ik
jk
a a
a =
For n
k j
i ,...
2 ,
1 ,
, =
j i
ij
w w
a =
26 From pairwise comparison matrix, relative priorities of the elements
compared are derived in the form of priority vector W. There are a number of ways to derive the vector of priorities W from the matrix
ij
a A
= . However,
emphasis on consistency led to an eigen value formulation below: W
W A
× =
×
max
λ where
max
λ is the maximum eigen value of matrix. The solution was obtained by raising the matrix to a sufficiently large
power, then summing over the rows and normalizing to obtain the priority vector
n
w w
w W
, ,
,
2 1
K =
. The process was stopped when the difference between components of the priority vector obtained at k
th
power and at the k+1
th
power had been less than some predetermined small value.
max
λ is always greater than or equal to n for positive, reciprocal matrices, and is equal to n if and only if A is a consistent matrix. Thus,
max
λ provides useful measure of the degree of inconsistency. Hereby,
,
max i
j ij
w w
a Σ
= λ
for j=1,2,…,n Normalizing this measured by the size of the matrix, consistency index
CI was defined as 1
max
− −
= n
n CI
λ
For each size of matrix n, random matrices were generated and their mean value, called as the random index RI was computed. These values were
illustrated in table 3.10. Using these values, the consistency ratio CR was defined as the ratio of CI to the RI. CR is a measure of how a given matrix
compared to a purely random matrix in terms of their CI’s. Therefore:
RI CI
CR =
27 Table 2. Random Consistency Index
n 1 2 3 4 5 6
RI 0 0.58 0.90 1.12 1.24
n 7 8 9 10
11 12
RI 1.32 1.41 1.49 1.51 1.53 1.56
n= size of pairwise comparison matrix
A value of CI andor 1
. ≤
CR is typically considered acceptable. Larger value
required the decision maker to reduce the inconsistency by revising judgments.
When using ArcGIS Spatial Analysis for processing, it will be able to access existing raster datasets and create new ones. It is important to understand
how raster data is represented in ArcGIS Spatial Analysis, how the ArcGIS Spatial Analysis functions alter the input data, and how the characteristics of the
input data and the settings it apply would affect the output data.
3.2.5.2. Alternative Scoring
Kategori