There are various approaches to weight and transform input criteria when performing overlay analysis. Each approach implements some permutation of the general overlay analysis steps which are most commonly used in suitability modeling.

- Define the problem.
- Break the problem into submodels.
- Determine significant layers.
- Reclassify or transform the data within a layer.
- Weight the input layers.
- Add or combine the layers.
- Select the best locations.
- Analyze.

The three main approaches available to weight and add the transformed input criteria—steps 5 and 6—are Weighted Overlay, Weighted Sum, and Fuzzy Overlay. Each approach has different basic premises and assumptions. The most appropriate approach is dependent on the particular problem being solved. A summary of each follows.

## Weighted Overlay

In Weighted Overlay analysis, a series of tools can complement the Weighted Overlay tool to follow the general overlay analysis steps described above. The Weighted Overlay tool scales the input data on a defined scale (the default being 1 to 9), weights the input rasters, and adds them together. The more favorable locations for each input criterion will be reclassed to the higher values such as 9. In the Weighted Overlay tool, the weights assigned to the input rasters must equal 100 percent. The layers are multiplied by the appropriate multiplier, and for each cell, the resulting values are added together. Weighted Overlay assumes that more favorable factors result in the higher values in the output raster, therefore identifying these locations as being the best.

## Weighted Sum

Weighted Sum overlay analysis follows the same general steps of the overlay analysis described above. Using the Weighted Sum tool, complemented by other Spatial Analyst tools, an additive overlay analysis can be implemented. The values for the input layers need to be reclassified prior to using the Weighted Sum tool. Unlike the weights in the Weighted Overlay tool, the weights assigned to the input rasters can be any value and do not need to add to a specific sum. When adding the input rasters, the Weighted Sum tool output values are a direct result of the addition of the multiplication of each value by the weights. Unlike Weighted Overlay, the values are not rescaled back to a defined scale; therefore, it maintains the attribute resolution of the values entered in the model. Weighted Sum assumes that more favorable factors result in the higher values in the final output raster, therefore identifying these locations as being the best.

## Fuzzy Overlay

Fuzzy Overlay analysis is based on set theory. Set theory is the mathematical discipline quantifying the membership relationship of phenomena to specific sets. In Fuzzy Overlay, a set generally corresponds to a class. The Fuzzy Membership and Fuzzy Overlay tools are used to peform this type of analysis.

Fuzzy Overlay loosely follows the general overlay analysis steps discussed above but differs in the meaning of the reclassed values and the results from combining the multiple criteria. The first three steps are the same: define the problem, break it into submodels, and determine significant layers. Like Weighted Overlay and Weighted Sum above, Fuzzy Overlay analysis reclassifies or transforms the data values to a common scale, but the transformed values define the possibility of belonging to a specified set, such as the slope values, being transformed into the possibility of belonging to the favorable suitability set (from 0 to 1, with 1 definitely being a member of the set). In Weighted Overlay and Weighted Sum, the values are on a ratio scale of preference, with the higher values being more favorable, unlike possibilities of membership as they are in Fuzzy Overlay.

Since the transformed values represent possibilities of membership to sets, in Fuzzy Overlay analysis, the input rasters are not weighted. In the add and combine step (see list above) of the general overlay analysis, Fuzzy Overlay differs from Weighted Overlay and Weighted Sum. The combining analysis step in Fuzzy Overlay analysis quantifies each location's possibility of belonging to specified sets from various input rasters.