EXERCISE 2-9 MCE: ORDERED WEIGHTED AVERAGING 134
Clearly the OWA technique can produce results that are very similar to the AND, OR, and WLC results. In a way these are all subsets of OWA. However, because we can alter the order weights in terms of their skew and dispersion, we can produce an almost infinite range of possible solutions to our residential development problem, i.e., solutions that fall anywhere along the continuum from AND to OR and that have varying levels of tradeoff.
For example, in our residential development problem, town planners may be interested in a conservative or low-risk solution for identifying suitable areas for development. However, they also know that their estimates for how different factors should trade off with each other are also important and should be considered. The AND operation will not let them consider any tradeoff, and the WLC operation, where they would have full tradeoff, is too liberal in terms of risk. They will then want to develop a set of order weights that would give them some amount of tradeoff but would maintain a level of low risk in the solution.
There are several sets of order weights that could be used to achieve this. For low risk, the weight should be skewed to the minimum end. For some tradeoff, weights should be distributed through all ranks. The following set of order weights was used to create the image
MCEMIDAND.
Low Level of Risk - Some Tradeoff
Order Weights: 0.5 0.3 0.125 0.05 0.025 0.0
Rank: 1st 2nd 3rd 4th 5th 6th
Notice that these order weights specify an operation midway between the extreme of AND and the average risk position of WLC. In addition, these order weights set the level of tradeoff to be midway between the no tradeoff situation of the AND operation and the full tradeoff situation of WLC.
G
Display the image MCEMIDAND from the group file called MCEMIDAND. (The remaining MCE output images have already been created for you.H
Display the image MCEMIDOR from the group file called MCEMIDOR. The following set of order weights was used to create MCEMIDOR.High Level of Risk - Some Tradeoff
Order Weights: 0.0 0.025 0.05 0.125 0.3 0.5
Rank: 1st 2nd 3rd 4th 5th 6th
5
How do the results from MCEMIDOR differ from MCEMIDAND in terms of tradeoff and risk? Would the MCEMIDOR result meet the needs of the town planners?EXERCISE 2-9 MCE: ORDERED WEIGHTED AVERAGING 135
6
In a graph similar to the risk-tradeoff graph above, indicate the rough location for both MCEMIDAND and MCEMIDOR.I
Close all open display windows and display all five results from the OWA procedure in order from AND to OR (i.e., MCEMIN, MCEMIDAND, MCEAVG, MCEMIDOR, MCEMAX), into the same map window. Then use the Identify tool to explore the values in these images. It may be easier to use the graphic display in the Identify box. To do so, click on the View as Graph button at the bottom of the box.While it is clear that suitability generally increases from AND to OR for any given location, the character of the increase between any two operations is different for each location. The extremes of AND and OR are clearly dictated by the minimum and maximum factor values, however, the results from the middle three tradeoff operations are determined by an averaging of factors that depends upon the combination of factor values, factor weights, and order weights. In general, in locations where the heavily weighted factors (slopes and roads) have similar suitability scores, the three results with tradeoff will be strikingly similar. In locations where these factors do not have similar suitability scores, the three results with tradeoff will be more influenced by the difference in suitability (toward the minimum, the average, or the maximum).
In the OWA examples explored so far, we have varied our level of risk and tradeoff together. That is, as we moved along the continuum from AND to OR, tradeoff increased from no tradeoff to full tradeoff at WLC and then decreased to no tradeoff again at OR. Our analysis, graphed in terms of tradeoff and risk, moved along the outside edges of a triangle, as shown in the figure below.
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However, had we chosen to vary risk independent of tradeoff we could have positioned our analysis anywhere within the triangle, the Decision Strategy Space.
Suppose that the no tradeoff position is desirable, but the no tradeoff positions we have seen, the AND (minimum) and OR (maximum), are not appropriate in terms of risk. A solution with average risk and no tradeoff would have the following order weights.
Average Level of Risk - No Tradeoff
Order Weights: 0.0 0.0 0.5 0.5 0.0 0.0 Rank: 1st 2nd 3rd 4th 5th 6th
EXERCISE 2-9 MCE: ORDERED WEIGHTED AVERAGING 136
(Note that with an even number of factors, setting order weights to absolutely no tradeoff is impossible at the average risk position.)
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Where would such an analysis be located in the decision strategy space?J
Display the image called MCEARNT (for average risk, no tradeoff). Compare MCEARNT with MCEAVG. (If desired, you can add MCEARNT to the MCEOWA group file by opening the group file in TerrSet Explorer, adding MCEARNT, then saving the file.)MCEAVG and MCEARNT are clearly quite different from each other even though they have identical levels of risk. With no tradeoff, the average risk solution, MCEARNT, is near the median value instead of the weighted average as in MCEAVG (and MCEWLC). As you can see, MCEARNT breaks significantly from the smooth trend from AND to OR that we explored earlier. Clearly, varying tradeoff independently from risk increases the number of possible outcomes as well as the potential to modify analyses to fit individual situations.