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GIS have capability to store and analyze spatial data effectively, and it could be spatial modeling to support decision analysis Center for GIS, 2005.
GIS has long experience in decision making and map design, and it can integrate with MCDA system to support decision makers Zhao and Garner, 2009.
The goal of spatial MCDM is to achieve solutions for spatial decision problems that take the input from multiple criteria. These criteria, also called
attribute have to be identified very carefully to ensure that the final goal could be achieved Prakash, 2003 in Dewi, 2008.
Spatial data analysis is in many ways the most important part of Geography Information System GIS, because it includes all of the
transformations, manipulations, and methods that can be applied to geographic data to add value to them, to support decision, and to reveal patterns and
anomalies that are not immediately obvious. It is desirable that the geographical data management and analysis component contain a robust set of tools that are
available in full fledged GIS system Malczewski, 1999. Method of analysis used MCDA approach for priority development area of
rubber plantation criteria which is integrated with GIS. Assigning weighted value for criteria use Weighted Linear Combination WLC as described in equation 1
and Pair-wise Comparison Method PCM.
2.7 Analytical Hierarchy Process AHP
Analytical Hierarchy Process AHP is a decision making approach developed by Saaty in 1980. The principles utilized in AHP to solve problems are
to construct hierarchies. The hierarchy allows for the assessment of the contribution individual criterion at lower levels to make criterion at higher levels
of the hierarchy. The decision making in AHP is a process that continuous from analyzing
the decision environment to understand and arrange the criteria into different groups and levels that reach the evaluation of the criteria in its decision outputs
Saaty, 1980. The AHP includes procedures and principles used to synthesize the
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many judgments to derive priorities among criteria and down to alternative solution. AHP has several basic steps to be employed as follows Saaty, 1980:
1. identify the problem and determine the goal,
2. structure the hierarchy from the top,
3. construct a set of pair wise comparison matrices,
4. there are nn-12 judgments required to develop each matrix in step 3,
5. determined the consistency using the Eigen value,
6. horizontal processing,
7. vertical processing,
8. Calculate the consistency ratio.
The AHP has three basic steps for considering decision problems by AHP. It begins by decomposing the overall goal suitability into a number of criteria
and sub-criteria. The goal itself represents the top level of the hierarchy. Major criteria comprise two level, sub-criteria make up level three, and so on.
Each land mapping unit is an area which has common land-use characteristics. Sustainable evaluation of development area requires evaluate not
only natural physical conditions but also socio-economic conditions. In order to determine which criteria and at what levels or weights affect development for
each land-use type, experts are consulted to provide judgments on important of criteria. Using AHP technique these judgments on importance of criteria are
converted to criteria weights w
i
. Score for each criterion x
i
on each land mapping unit is then determined. The weighted linear combination of w
i
and x
i
give suitability index for each land mapping unit. By the above process, development area for rubber plantation map is produced.
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The largest Eigen value is equal to the size of comparison matrix, or . Then calculate a measure of consistency, called Consistency Index as
deviation or degree of consistency using the following formula. 2
After knowing the Consistency Index, the next question is how do we use this index? Prof. Saaty proposed that we use this index by comparing it
with the appropriate one. The appropriate Consistency index is called Random Consistency Index RI. The random consistency index should be 10 or less,
random consistency index of sample size 500 matrices is used. The average random consistency index of sample size 500 matrices is shown in the Table 5.
Table 5 Random Consistency Index RI n
1 2
3 4
5 6
7 8
9 10 RI
0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 Some experiences in AHP process, the values of the pair wise comparison
matrix will normally be well considered and not set arbitrarily. However, people’s feeling and preferences remain inconsistent and intransitive and may then lead to
perturbations in the eigenvector calculations Marinoni, 2004. Saaty 1986 defined a consistency ratio CR as a ratio of the consistency index CI to an
average consistency index RI, thus; 3
RI or resulting average consistency index, also called the random index, was calculated by Saaty 1986 as the average consistency of square matrices of
various orders n which he filled with random entries. The consistency ratio CR should be about 10 or less to be acceptable.
If the CR does not fall in the required range, the quality of the judgments should be improved.
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2.8 Rating Absolute Measurement
