Available with Spatial Analyst license.

## Summary

Defines a fuzzy membership through a function based on the mean and standard deviation, with the smaller values having a membership closer to 1.

## Discussion

The tool that uses the FuzzyMSSmall object: Fuzzy Membership.

There are two equations for the MS Small function, depending on the product of a * m.

- If x > a * m:
`u(x) = (b * s) / (x - (a * m) + (b * s))`

- where:
m = the mean

s = the standard deviation

a = a multiplier of the mean

b = a multiplier of the standard deviation

The a and b multipliers are input parameters.

- where:
- If x <= a * m:
`u(x) = 0`

The MSSmall function is useful when the small input values have a higher membership.

The input values can be either integer or floating point positive values.

The result can be similar to the Small fuzzy membership function, depending on how the multipliers of the mean and standard deviation are defined.

## Syntax

FuzzyMSSmall (meanMultiplier, STDMultiplier)

Parameter | Explanation | Data Type |

meanMultiplier | The multiplier for the mean of the input values in the MSLarge function equation. (The default value is 1) | Double |

STDMultiplier | The multiplier for the standard deviation of the input values in the MSLarge function equation. (The default value is 1) | Double |

## Properties

Property | Explanation | Data Type |

meanMultiplier (Read and Write) | The multiplier for the mean of the input values in the membership function equation. | Double |

STDMultiplier (Read and Write) | The multiplier for the standard deviation of the input values in the membership function equation. | Double |

## Code Sample

##### FuzzyMSSmall example 1 (Python window)

Demonstrates how to create a FuzzyMSSmall class and use it in the FuzzyMembership tool within the Python window.

```
import arcpy
from arcpy.sa import *
from arcpy import env
env.workspace = "c:/sapyexamples/data"
outFzyMember = FuzzyMembership("as_std", FuzzyMSSmall(1.2, 3.2))
outFzyMember.save("c:/sapyexamples/fzymssml")
```

##### FuzzyMSSmall example 2 (stand-alone script)

Performs a FuzzyMembership using the FuzzyMSSmall class.

```
# Name: FuzzyMSSmall_Ex_02.py
# Description: Scales input raster data into values ranging from zero to one
# indicating the strength of a membership in a set.
# 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
inRaster = "as_std"
# Create the FuzzyMSSmall algorithm object
meanMultiply = 1.5
stdMultiply = 1
myFuzzyAlgorithm = FuzzyMSSmall(meanMultiply, stdMultiply)
# Check out the ArcGIS Spatial Analyst extension license
arcpy.CheckOutExtension("Spatial")
# Execute FuzzyMembership
outFuzzyMember = FuzzyMembership(inRaster, myFuzzyAlgorithm)
# Save the output
outFuzzyMember.save("c:/sapyexamples/fzymssml2")
```