# An overview of fuzzy classes

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.

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

Tools that use the fuzzy objects

FuzzyMembership

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

FuzzyOverlay

7/16/2013