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Weighted Linear Combination

Weighted linear combination is the most often used technique for tackling spatial multiattribute decision making. It is a multiattribute procedure based on the concept of a weighted average. The decision maker directly assigns weights of relative importance to each attribute. A total score is then obtained for each alternative by multiplying the importance weigth assigned for each attribute by the scaled value given to the alternative on that attribute, and summing the products over all attributes. When the oval scores are calculated for all the alternatives, the alternative with the highest overall score is chosen. The GIS-based linear combination method involves the following steps:

1. Define the set of evaluation criteria (map layers) and the set fo feasible alternatives.
2. Standardize each criterion map layer.
3. Define the criterion weights; that is, a weight of relative importance is directly assigned to each criterion map.
4. Construct the weighted standardized map layers; that is, multiply standardized map layers by the corresponding weights.
5. Generate the overall score for each alternative using the add overlay operation on the weighted standardized map layers.
6. Rank the alternatives according to the overall performance scores; the alternative with the highest score (rank) is the best alternative.

The weighted linear combination method can be operationalized using any GIS system having overlay capabilities. The overlay techniques allow the evaluation criterion map layers (input maps) to be aggregated to determine the composite map layer (output maps). The method can be implemented in both raster and vector GIS environments.

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