# An overview of fuzzy classes

Available with Spatial Analyst license.

The fuzzy classes are used to define the transformation or remap of the input values to new values based on a specified function. The transformation process is referred to as fuzzification and establishes the fuzzy membership for each input value. The transformed values range from 0 to 1, defining the possibility of membership to a specified class or set, with 1 being absolutely in the set. Each fuzzy class defines a continuous function, and each function captures a different type of transformation to achieve a desired effect. For example, one function is more appropriate when the values closer to a specified value have a higher possibility of being a member of the set, while another function might be more appropriate if the higher values are more likely to be members of the set.

Class | Description |
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FuzzyGaussian | Defines a fuzzy membership function through a Gaussian or normal distribution based around a user-specified midpoint (which is assigned a membership of 1) with a defined spread decreasing to zero. |

FuzzyLarge | Defines a fuzzy membership function where the larger input values have membership closer to 1. The function is defined by a user-specified midpoint (which is assigned a membership of 0.5) with a defined spread. |

FuzzyLinear | Defines a fuzzy membership function through a linear transformation between the user-specified minimum value, a membership of 0, to the user-defined maximum value, which is assigned a membership of 1. |

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

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

FuzzyNear | Defines a fuzzy membership function around a specific value which is defined by a user-defined midpoint (which is assigned a membership of 1), with a defined spread decreasing to zero. |

FuzzySmall | Defines a fuzzy membership function with the smaller input values having membership closer to 1. The function is defined by a user-specified midpoint (which is assigned a membership of 0.5) with a defined spread. |

The following tool uses the fuzzy objects:

Once several input rasters have been transformed, the relationship between the different transformed rasters can be established and analyzed with the following tool:

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