# Fuzzy Overlay (Spatial Analyst)

## Summary

Combine fuzzy membership rasters data together, based on selected overlay type.

## Usage

• This tool is recommended for the use with the result of fuzzy membership tool. It is meant to be applied to rasters with values that range between 0 and 1.

• The following lists the appropriate Overlay type to use for certain conditions.

• Use OR when any of the input evidence rasters can have a high value in order for the output to be a high value.
• Use AND when all of the input evidence rasters must have a high value in order for the output to be a high value.
• Use PRODUCT when the combined evidence is less important than any single evidence.
• Use SUM when the combined evidence is more important than any single evidence.

• The GAMMA Overlay type is typically used to combine fuzzy combinations of more basic data. When Gamma is 1 the result is the same as Fuzzy Sum. When Gamma is 0 the result is the same as Fuzzy Product. Values in between allow the user to combine evidence between these two extremes and possibly different than Fuzzy And or Fuzzy Or.

## Syntax

FuzzyOverlay (in_rasters, {overlay_type}, {gamma})
 Parameter Explanation Data Type in_rasters[in_raster,...] A list of input membership rasters to be combined in the overlay. Raster Layer overlay_type(Optional) Specifies the method used to combine two or more membership data. AND —The minimum of the fuzzy memberships from the input fuzzy rasters. OR —The maximum of the fuzzy memberships from the input rasters. PRODUCT — A decreasive function. Use this when the combination of multiple evidence is less important or smaller than any of the inputs alone. SUM —An increasive function. Use this when the combination of multiple evidence is more important or larger than any of the inputs alone. GAMMA — The algebraic product of the Fuzzy Sum and Fuzzy Product, both raised to the power of gamma. String gamma(Optional) The gamma value to be used. This is only when the Overlay type is set to GAMMA.Default value is 0.9. Double

#### Return Value

 Name Explanation Data Type out_raster The output raster which is the results of applying the fuzzy operator.This output will always have a value between 0 and 1. Raster

## Code Sample

FuzzyOverlay example 1 (Python window)

This example combines the input membership rasters with the AND overlay type to identify the minium membership value between them.

```import arcpy
from arcpy.sa import *
from arcpy import env
env.workspace = "c:/sapyexamples/data"
outFzyOverlay = FuzzyOverlay(["fzymembout1", "fzymembout2"], "AND")
outFzyOverlay.save("c:/sapexamples/output/fuzzover.tif")
```
FuzzyOverlay example 2 (stand-alone script)

This example combines the input membership rasters with a GAMMA overlay type.

```# Name: FuzzyOverlay_Ex_02.py
# Description: Combine fuzzy membership rasters data together based on
#    selected overlay type ("GAMMA" in this case).
# Requirements: Spatial Analyst Extension

# Import system modules
import arcpy
from arcpy import env
from arcpy.sa import *

# Set environment settings
env.workspace = "C:/sapyexamples/data"

# Set local variables
inRasterList = ["fzymembout1", "fzymembout2"]

# Check out the ArcGIS Spatial Analyst extension license
arcpy.CheckOutExtension("Spatial")

# Execute FuzzyMembership
outFzyOverlay = FuzzyOverlay(inRasterList, "GAMMA", 0.9)

# Save the output
outFzyOverlay.save("c:/sapexamples/output/fuzzoverlay")
```

## Licensing Information

ArcGIS for Desktop Basic: Requires Spatial Analyst
ArcGIS for Desktop Standard: Requires Spatial Analyst
ArcGIS for Desktop Advanced: Requires Spatial Analyst
11/8/2012