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Fuzzy Membership and Overlay, Weighted Overlay and Weighted Sum

Husam Jubeh
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Fuzzy Membership and Overlay, Weighted Overlay and Weighted Sum Tools

Fuzzy Membership

How to use Fuzzy Membership Tool in Arc Toolbox??

Fuzzy Membership Tool
Fuzzy Membership

Path to access the tool

:

Fuzzy Membership Tool, Overlay Toolset, Spatial Analyst Tools Toolbox

 

Fuzzy Membership

Transforms the input raster into a 0 to 1 scale, indicating the strength of a membership in a set, based on a specified fuzzification algorithm.

A value of 1 indicates full membership in the fuzzy set, with membership decreasing to 0, indicating it is not a member of the fuzzy set.

1. Input raster

The input raster whose values will be scaled from 0 to 1.

It can be an integer or a floating-point raster.

2. Output raster

The output will be a floating-point raster with values ranging from 0 to 1.

3. Membership type (optional)

Specifies the algorithm used in fuzzification of the input raster.

Certain settings for Membership type employ a Spread parameter to determine how rapidly the fuzzy membership values decrease from 1 to 0. The default values for the spread are detailed in the table below.

Gaussian—Assigns a membership value of 1 at the midpoint.The membership decreases to 0 for values that deviate from the midpoint according to a normal curve. Gaussian is similar to the Near function but has a more narrow spread.

  • Midpoint — Default is the midpoint of the range of values of the input raster.

  1. Spread — Default is 0.1. Typically, the values vary between [0.01–1].
  2. Small—Used to indicate that small values of the input raster have high membership in the fuzzy set.Assigns a membership value of 0.5 at the midpoint.
  3. Midpoint — Default is the midpoint of the range of values of the input raster.
  4. Spread — Default is 5.

  • Large—Used to indicate that large values of the input raster have high membership in the fuzzy set.Assigns a membership value of 0.5 at the midpoint.
  1. Midpoint — Default is the midpoint of the range of values of the input raster.
  2. Spread — Default is 5.

  • Near—Calculates memberships for values near some intermediate value.Assigns a membership value of 1 at the midpoint. The membership decreases to 0 for values that deviate from the midpoint.
  1. Midpoint — Default is the midpoint of the range of values of the input raster.
  2. Spread — Default is 0.1. Typically, the values vary within the range of [0.001–1].

  • MSLarge—Calculates membership based on the mean and standard deviation of the input data where large values have high membership. The result can be similar to the Large function, depending on how the multipliers of the mean and standard deviation are defined.
  1. Mean multiplier — Default is 1.
  2. Standard deviation multiplier — Default is 2.

  • MSSmall—Calculates membership based on the mean and standard deviation of the input data where small values have high membership. This is the default membership type. The result can be similar to the Small function, depending on how the multipliers of the mean and standard deviation are defined.
  1. Mean multiplier — Default is 1.
  2. Standard deviation multiplier — Default is 2.

  • Linear—Calculates membership based on the linear transformation of the input raster. Assigns a membership value of 0 at the minimum and a membership of 1 at the maximum.
  1. Minimum — Default is 1.
  2. Maximum — Default is 2.

4. Hedge (optional)

Defining a hedge increases or decreases the fuzzy membership values which modify the meaning of a fuzzy set. Hedges are useful to help in controlling the criteria or important attributes.

  1. NONE—No hedge is applied. This is the default.
  2. SOMEWHAT—Known as dilation, defined as the square root of the fuzzy membership function. This hedge increases the fuzzy membership functions.
  3. VERY—Also known as concentration, defined as the fuzzy membership function squared. This hedge decreases the fuzzy membership functions.

Fuzzy Overlay

How to use Fuzzy Overlay Tool in Arc Toolbox??

Fuzzy Overlay Tool
Fuzzy Overlay

Path to access the tool

:

Fuzzy Overlay Tool, Overlay Toolset, Spatial Analyst Tools Toolbox

 

Fuzzy Overlay

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

1. Input rasters

A list of input membership rasters to be combined in the overlay.

2. 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.

3. Overlay type (optional)

Specifies the method used to combine two or more membership data.

  1. AND—The minimum of the fuzzy memberships from the input fuzzy rasters.
  2. OR—The maximum of the fuzzy memberships from the input rasters.
  3. PRODUCT—A decreasive function. Use this when the combination of multiple evidence is less important or smaller than any of the inputs alone.
  4. SUM—An increasive function. Use this when the combination of multiple evidence is more important or larger than any of the inputs alone.
  5. GAMMA—The algebraic product of the fuzzy SUM and fuzzy PRODUCT, both raised to the power of gamma.

4. 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.

Weighted Overlay

How to Weighted Overlay Tool in Arc Toolbox ArcMap ArcGIS??

Weighted Overlay Tool
Weighted Overlay

Path to access the tool

:

Weighted Overlay Tool, Overlay Toolset, Spatial Analyst Tools Toolbox

 

Weighted Overlay

Overlays several rasters using a common measurement scale and weights each according to its importance.

1. Weighted overlay table

The weighted overlay table allows the calculation of a multiple-criteria analysis between several rasters.

Table:

  1. Raster—The input criteria raster being weighted.
  2. % Influence—The influence of the raster compared to the other criteria as a percentage of 100. Values are rounded down to the nearest integer. The sum of influences must equal 100.
  3. Field—The field of the criteria raster to use for weighting.
  4. Scale Value—The scaled value for the criterion, as specified by the Evaluation scale setting. Changing these values will alter the values in the input rasters used in the overlay analysis. You can enter a value directly or select from the drop-down list. In addition to numerical values, the following options are available:
  • Restricted—Assigns the restricted value (the minimum value of the evaluation scale set, minus one) to cells in the output, regardless of whether other input rasters have a different scale value set for that cell.
  • NoData—Assigns NoData to cells in the output, regardless of whether other input rasters have a different scale value set for that cell.

2. Evaluation scale—Select from a list of predefined evaluation scales. You can also define your own evaluation scale with the From, To, and By controls.

3. Set Equal Influence—Balances the percent influence of the input rasters equally and sums them to 100.

4. Output raster

The output weighted raster.

Weighted Sum

How to use Weighted Sum Tool in Arc Toolbox??

Weighted Sum Tool
Weighted Sum

Path to access the tool

:

Weighted Sum Tool, Overlay Toolset, Spatial Analyst Tools Toolbox

 

Weighted Sum

Overlays several rasters, multiplying each by their given weight and summing them together.

1. Input rasters

The weighted sum table allows you to apply different weights to individual input rasters before they are summed together.

  1. Raster—The raster being weighted.
  2. Field—The field of the raster to use for weighting.
  3. Weight—The weight value by which to multiply the raster. It can be any positive or negative decimal value.

2. Output raster

The output weighted raster.

It will be of floating-point type.

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