ANALYTICAL HIERARCHY PROCESS (AHP)
Applying AHP in Weighting GIS Model Criteria
The following extends the brief description in the Beyond Mapping column on “Calibrating and Weighting GIS Model Criteria” by Joseph K. Berry appearing in GeoWorld, September, 2003. The columns in this series are posted at— http://www.innovativegis.com/basis/MapAnalysis/Default.html, select Topic 19, Routing and Optimal Paths.
A companion discussion
on applying the
What is AHP?
Analytical Hierarchy process (AHP) is a quantitative method for ranking decision alternatives by developing a numerical score to rank each decision alternative based on how well each alternative meets the decision maker’s criteria (Operations Management, 4th Edition, 2003, by R. Russell and B. Taylor, Prentice-Hall).
What kind of information is gained?
AHP can be used to determine the relative weights among decision elements for GIS-based Suitability and Routing models. In its many other applications AHP is used to select the best single alternative that best matches decision criteria (decision-making models).
What is involved in the process?
The process involves 1) identifying the decision elements (map layers), 2) recording relative importance of those elements, 3) construction of an importance table and 4) implementing a simple mathematical solution.
For example, the routing of an electric transmission line described in the Beyond Mapping series (see above reference) is used to demonstrate the process in the following paragraphs.
How are the decision elements identified?
The decision elements are identified by group interaction and discussion. The Delphi Process can be useful in identifying and calibrating the decision elements.
In the transmission line routing example, the objectives and map layers include avoiding locations that 1) have high Visual Exposure (VE= Visual_Exposure_rating), 2) are close to Sensitive Areas (SA= SA_Proximity_rating), 3) are far from Roads (R= R_Proximity_rating) and 4) have high Housing Density (HD= H_Density_rating).
How are the pairwise comparisons recorded?
For example, a group member might respond to the question “In routing electric transmission lines…”
(VE vs. SA)— avoiding locations of high Visual Exposure is extremely more important (rating= 9) than avoiding locations close to Sensitive Areas.
(VE vs. R)— avoiding locations of high Visual Exposure is strongly more important (rating= 5) than avoiding locations close to Roads.
(VE vs. HD)— avoiding locations of high Visual Exposure is equally important (rating= 1) to avoiding locations of high Housing Density.
(SA vs. R)— avoiding locations close to Roads is strongly to very strongly more important (rating= 6) than avoiding locations close to Sensitive Areas.
(SA vs. HD)— avoiding locations of high Housing Density is very strongly to extremely more important (rating= 8) than avoiding locations close to Sensitive Areas.
(R vs. HD)— avoiding locations of high Housing Density is strongly more important (rating= 5) than avoiding locations close to Roads.
How is an individual importance table constructed?
For example, the first response noted above identifies that VE is extremely (9) more important than SA so the value 9 is placed in position row 2, column 3. The reciprocal value of 1/9 (.111) is placed in position row 3, column 2. The last response identifies that HD is strongly (5) more important than R so the value 5 is placed in row 5, column 4; the reciprocal 1/5 (.200) is placed in row 4, column 5.
How are the weights calculated?
Enter pairwise responses into the importance table.
Step 1: Complete the table by calculating the reciprocal values.
Step 3: Sum the column values.
Step 4: Normalize the table values by dividing by the column sums.
Step 5: Sum the normalized row values.
***Note: Complete Steps 1 through 4 for each participant and average the weight sets, then determine the minimum value before proceeding to Step 6.
Step 6: Divide the row sums by minimum value for relative weights.
Importance of avoiding locations—
…of high Visual Exposure (VE) is 10.64 times more important than avoiding locations near Sensitive Areas (SA)
…far from Roads (R) is 3.23 times more important than avoiding locations near Sensitive Areas (SA)
…of high Housing Density (HD) is 10.38 times more important than avoiding locations near Sensitive Areas (SA).
How are the derived weights utilized in a GIS model?
What information is gained?
The tables at the bottom of the figure summarize the data from the criteria maps. Note the average values for Visual Exposure (VE= 9.1 vs. 3.6), proximity to Sensitive Areas (SA= 11.7 vs. 5.6), proximity to Roads (R= 8.4 vs. 11.7) and Housing Density (HD= 18.7 to 3.0). The statistics confirm that the Community route tends to avoid high visual exposure and housing density, while the Environmental route tends to avoid being close to sensitive areas. Both routes have similar proximity to roads values.