# 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 the 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 to get the maximum value from all of the input evidence rasters. In this case, if any of the input have a high value, the final output will be high.
• Use And to get the minimum value from all of the input evidence rasters. Here, all inputs 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 type is typically used to combine more basic data. When gamma is 1, the result is the same as fuzzy sum. When it is 0, the result is the same as fuzzy Product. Values between 0 and 1 allow you to combine evidence to produce results between the two extremes established by fuzzy And or Fuzzy Or.

• See Analysis environments and Spatial Analyst for additional details on the geoprocessing environments that apply to this tool.

## Parameters

 Label Explanation Data Type Input rasters 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 available when the Overlay type is set to Gamma.Default value is 0.9. Double

### Return Value

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

`FuzzyOverlay(in_rasters, {overlay_type}, {gamma})`
 Name 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 available 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 result 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"]

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

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

## Licensing information

• Basic: Requires Spatial Analyst
• Standard: Requires Spatial Analyst