GIS and Decision-making Gis as a decision making tool Decision Strategies in GIS

GIS and Decision-making

Gis as a decision making tool

Decision Strategies in GIS

We commonly use GIS to assist in the process of decision making. However, few of us realize how our software systems may be giving our decisions an unexpected character. For example, consider the simple Boolean intersection operator - a mainstay of multi-criteria decision making. Perhaps we are seeking land development opportunities and have established desirable criteria as being near to main roads, on low slopes, and unforested. Assuming these have been developed as Boolean layers (simple true/false binary layers), the logical AND of the intersection operator would then produce a layer that showed all areas that met these three conditions - a straightforward, but very risk averse solution.

Risk averse? Yes. The intersection operator is a very hard decision strategy. If any condition is missed, it is immediately removed from consideration, no matter how stellar its other attributes might be. While this may be appropriate in some instances, it may also be more limiting than we might wish. Further, the result may be very different from one achieved through a different approach. For example, Weighted Linear Combination is another common strategy for evaluating multi-criteria decision problems. In this case, we rescale attributes to a common evaluation scale (e.g., a scale from 0 to 1, or perhaps 0 to 100), and then average the scores (often after applying an importance weight). This is considerably less risk averse. For example, having a very low slope might compensate for a location somewhat far from a road.

These two decision strategies dominate our use of GIS. However, recent developments in Decision Science suggest that a much wider range of strategies can be deployed. Perhaps the most flexible is a procedure known as the Ordered Weighted Average (OWA), recently introduced to GIS. This is a procedure that is somewhat related to Weighted Linear Combination, but which is capable of producing a virtually infinite variety of strategies as illustrated below.

The OWA procedure results in decision strategies that vary along two dimensions: risk and tradeoff. At one extreme, we have a solution which assumes the least risk possible and consequently allows no tradeoff (the lower left corner of this triangle). This corresponds most closely with the Boolean intersection operator and is, in fact, the same as the most commonly used fuzzy set intersection operator (the minimum operator). This result is illustrated by the upper-leftmost solution in Figure 2 (an evaluation of suitability for development based on proximity to roads and the town center, slope and distance from a protected nature reserve - green and yellows areas are best; red and blue are worst).

This is the most conservative solution (corresponding to the AND logical operation), since it characterizes locations by their worst qualities. To be suitable, all qualities must be good - no tradeoff of qualities is allowed. Thus this strategy represents a very hard AND operation.

At the other extreme is the solution at the lower-right of the triangle (illustrated by the right-most solution in Figure 2). This corresponds to the logical OR operation and is the most optimistic solution. In this case, locations are characterized by their best qualities, clearly with a necessary assumption of risk by the analyst (i.e., the risk that the poorer qualities that are ignored will adversely affect its actual performance as a solution). Note that this solution exactly corresponds with the Fuzzy Set union (maximum) operator.

The remaining corner of the triangle in Figure 1 (the apex) represents the standard Weighted Linear Combination solution. Here we have a case of full tradeoff, and consequently intermediate risk. Here poorer qualities are not ignored, but they can be compensated for. This is illustrated in the middle of the cascade of solutions in Figure 2.

So far, these illustrations are not unfamiliar. However, a glance at Figure 2 shows that many other solutions are possible. In fact, the cascade of solutions illustrated shows the effects of systematically varying the degree of risk and tradeoff in the solution. The progression from the left-most to the right-most solution in Figure 2 corresponds with a trajectory from the lower-left corner of the triangle in Figure 1, to the top of the triangle, and then back down to the lower-right. Thus we can see that it is possible to produce solutions that are strongly conservative (risk averse) but which allow some flexibility in trading off small imperfections by strong qualities in other factors (such as the second solution from the top in the cascade). Indeed, the OWA operator can produce any possibility within this triangle. For example, the solution in the lower-left corner of Figure 2 illustrates a case of intermediate risk (like the standard Weighted Linear Combination), but with no tradeoff. This characterizes features by their middle-most quality. It is similar to some scoring procedures in gymnastics competitions where the best and worst scores are thrown away.

In many respects, this triangular strategy space is similar to the concept of an investment portfolio. A portfolio of blue chip stocks would be found in the lower-left corner: a strategy that produces small but safe returns. The lower-right corner would represent a portfolio of high tech stocks - potentially high performers, but with considerable risk. Finally, a portfolio at the apex of the triangle would be like a mutual fund - a mixed portfolio intended to provide higher returns with some absorption of risk.

This is a new feature in GIS, and is thus not found in many systems. However, it offers a clear maturation of our ability to make effective decisions in the allocation of precious resources, and (as recent interest in the professional literature would suggest) it seems virtually certain that it will be found in others quite soon.